Temps locaux
[Local times ]
(Paris, 1976–1977 ).
Edited by J. Azéma and M. Yor .
Astérisque 52–53 .
Société Mathématique de France (Paris ),
1978 .
MR
509476 Zbl
0385.60063 book
People
BibTeX
@book {key509476m,
TITLE = {Temps locaux [Local times]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Ast\'erisque},
NUMBER = {52--53},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
ADDRESS = {Paris},
YEAR = {1978},
PAGES = {ii+223},
NOTE = {(Paris, 1976--1977). MR:509476. Zbl:0385.60063.},
ISSN = {0303-1179},
}
M. Yor :
“Sur la continuité des temps locaux associés à certaines semi-martingales ”
[On the continuity of local time associated with certain semi-martingales ],
pp. 23–26
in
Temps locaux
[Local times ]
(Paris, 1976–1977 ).
Edited by J. Azéma and M. Yor .
Astérisque 52–53 .
Société Mathématique de France (Paris ),
1978 .
With an English summary.
incollection
People
BibTeX
@incollection {key56931407,
AUTHOR = {Marc Yor},
TITLE = {Sur la continuit\'e des temps locaux
associ\'es \`a certaines semi-martingales
[On the continuity of local time associated
with certain semi-martingales]},
BOOKTITLE = {Temps locaux [Local times]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Ast\'erisque},
NUMBER = {52--53},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
ADDRESS = {Paris},
YEAR = {1978},
PAGES = {23--26},
NOTE = {(Paris, 1976--1977). With an English
summary.},
ISSN = {0303-1179},
}
J. Azéma and M. Yor :
“Une solution simple au problème de Skorokhod A simple solution to a problem of Skorokhod ],
pp. 90–115
in
Séminaire de probabilités XIII
[Thirteenth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 721 .
Springer (Berlin ),
1979 .
MR
544782 Zbl
0414.60055 incollection
Abstract
People
BibTeX
An explicit solution is given to Skorohod’s problem: given a distribution \( \mu \) with mean 0 and finite second moment \( \sigma^2 \) , find a (non randomized) stopping time \( T \) of a Brownian motion \( (X_t) \) such that \( X_T \) has the distribution \( \mu \) and \( \mathbb{E}[T]=\sigma^2 \) . It is shown that if \( S_t \) is the one-sided supremum of \( X \) at time \( t \) ,
\[ T=\inf\{t:S_t\geq \psi(X_t)\} \]
solves the problem, where \( \psi(x) \) is the barycenter of \( \mu \) restricted to \( [x,\infty) \) . The paper has several interesting side results, like explicit families of Brownian martingales, and a proof of the Ray–Knight theorem on local times.
@incollection {key544782m,
AUTHOR = {Az\'ema, Jacques and Yor, Marc},
TITLE = {Une solution simple au probl\`eme de
{S}korokhod [A simple solution to a
problem of {S}korokhod]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIII}
[Thirteenth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {721},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1979},
PAGES = {90--115},
DOI = {10.1007/BFb0070852},
URL = {http://www.numdam.org/item?id=SPS_1979__13__90_0},
NOTE = {MR:544782. Zbl:0414.60055.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
J. Azéma and M. Yor :
“Le problème de Skorokhod: Compléments à l’exposé précédent The problem of Skorokhod: Supplement to the previous talk ],
pp. 625–633
in
Séminaire de probabilités XIII
[Thirteenth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 721 .
Springer (Berlin ),
1979 .
This is a supplement to the preceding article in Séminaire de probabilités XIII 721 (1979)
MR
544832 Zbl
0414.60056 incollection
Abstract
People
BibTeX
@incollection {key544832m,
AUTHOR = {Az\'ema, Jacques and Yor, Marc},
TITLE = {Le probl\`eme de {S}korokhod: {C}ompl\'ements
\`a l'expos\'e pr\'ec\'edent [The problem
of {S}korokhod: {S}upplement to the
previous talk]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIII}
[Thirteenth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {721},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1979},
PAGES = {625--633},
DOI = {10.1007/BFb0070901},
URL = {http://www.numdam.org/item?id=SPS_1979__13__625_0},
NOTE = {This is a supplement to the preceding
article in \textit{S\'eminaire de probabilit\'es
XIII} \textbf{721} (1979). MR:544832.
Zbl:0414.60056.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
Séminaire de probabilités XIV Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580103 Zbl
0416.00014 book
People
BibTeX
@book {key580103m,
TITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {vii+546},
DOI = {10.1007/BFb0089463},
NOTE = {MR:580103. Zbl:0416.00014.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
J. Azéma, R. F. Gundy, and M. Yor :
“Sur l’intégrabilité uniforme des martingales continues On the uniform integrability of continuous martingales ],
pp. 53–61
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580108 Zbl
0442.60046 incollection
Abstract
People
BibTeX
The main result of this paper is the following: Let \( X \) be a martingale which is continuous and bounded in \( L^1 \) (both conditions are essential). Then \( X \) is uniformly integrable if and only if
\[ t\,\mathbb{P}\{X^*\gt t\}\quad\text{or equivalently}\quad t\,\mathbb{P}\{S(X)\gt t\} \]
tend to 0 as \( t\to\infty \) , where \( S(X) \) is the usual square function. The methods (using a good lambda inequality) are close to [Lenglart et al. 1980].
@incollection {key580108m,
AUTHOR = {Az\'ema, J. and Gundy, R. F. and Yor,
M.},
TITLE = {Sur l'int\'egrabilit\'e uniforme des
martingales continues [On the uniform
integrability of continuous martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {53--61},
DOI = {10.1007/BFb0089469},
URL = {http://www.numdam.org/item?id=SPS_1980__14__53_0},
NOTE = {MR:580108. Zbl:0442.60046.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
M. T. Barlow and M. Yor :
“Sur la construction d’une martingale continue, de valeur absolue donnée On the construction of a continuous martingale of given absolute value ],
pp. 62–75
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580109 Zbl
0426.60047 incollection
Abstract
People
BibTeX
This paper consists of two notes on Gilat’s theorem (Ann. Prob. 5 , 1977, see also [Maisonneuve 1979]). The problem consists in constructing, given a continuous positive submartingale \( Y \) , a continuous martingale \( X \) (possibly on a different space) such that \( |X| \) has the same law as \( Y \) . Let \( A \) be the increasing process associated with \( Y \) ; it is necessary for the existence of \( X \) that \( dA \) should be carried by \( \{Y=0\} \) . This is shown by the first note (Yor’s) to be also sufficient — more precisely, in this case the solutions of Gilat’s problem are all continuous. The second note (Barlow’s) shows how to construct a Gilat martingale by “putting a random \( \pm \) sign in front of each excursion of \( Y \) ”, a simple intuitive idea and a delicate proof.
@incollection {key580109m,
AUTHOR = {Barlow, M. T. and Yor, M.},
TITLE = {Sur la construction d'une martingale
continue, de valeur absolue donn\'ee
[On the construction of a continuous
martingale of given absolute value]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {62--75},
DOI = {10.1007/BFb0089470},
URL = {http://www.numdam.org/item?id=SPS_1980__14__62_0},
NOTE = {MR:580109. Zbl:0426.60047.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
M. Yor :
“Application d’un lemme de T. Jeulin au grossissement de la filtration brownienne Application of a lemma of T. Jeulin to the enlargement of the Brownian filtration ],
pp. 189–199
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ],
vol. 784 .
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580123 Zbl
0427.60041 incollection
Abstract
People
BibTeX
The problem considered here is the smallest enlargement of the Brownian filtration for which the process
\[ \int_t^{\infty} B_s\,\mu(ds) \]
is adapted, \( \mu \) being a probability measure with a finite first moment.
@incollection {key580123m,
AUTHOR = {Yor, M.},
TITLE = {Application d'un lemme de {T}. {J}eulin
au grossissement de la filtration brownienne
[Application of a lemma of {T}. {J}eulin
to the enlargement of the {B}rownian
filtration]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
VOLUME = {784},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {189--199},
DOI = {10.1007/BFb0089484},
URL = {http://www.numdam.org/item?id=SPS_1980__14__189_0},
NOTE = {MR:580123. Zbl:0427.60041.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
J. Auerhan, D. Lépingle, and M. Yor :
“Construction d’une martingale réelle continue, de filtration naturelle donnée Construction of a real continuous martingale, of given natural filtration ],
pp. 200–204
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580124 Zbl
0432.60056 incollection
Abstract
People
BibTeX
It is proved in [Dellacherie and Stricker 1977] that, under a mere separability assumption, any filtration is the natural filtration of some bounded left-continuous increasing process \( (A_t) \) . If the filtration contains a Brownian motion \( (B_t) \) , then it is also the natural filtration of the continuous martingale
\[ \int_0^t A_s \,dB_s .\]
Therefore, the natural filtration of (finitely or countably) many independent Brownian motions is generated by a single continuous martingale. Explicit constructions are discussed.
@incollection {key580124m,
AUTHOR = {Auerhan, J. and L\'epingle, D. and Yor,
M.},
TITLE = {Construction d'une martingale r\'eelle
continue, de filtration naturelle donn\'ee
[Construction of a real continuous martingale,
of given natural filtration]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {200--204},
DOI = {10.1007/BFb0089485},
URL = {http://www.numdam.org/item?id=SPS_1980__14__200_0},
NOTE = {MR:580124. Zbl:0432.60056.},
ISSN = {0075-8434},
ISBN = {3540097600},
}
M. Yor :
“Remarques sur une formule de Paul Lévy Remarks on a formula of Paul Lévy ],
pp. 343–346
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580140 Zbl
0429.60045 incollection
Abstract
People
BibTeX
Given a two-dimensional Brownian motion \( (X_t,Y_t) \) , Lévy’s area integral formula gives the characteristic function
\[ \mathbb{E}\Bigl[ \exp\Bigl( iu\int_0^1 X_s\,dY_s-Y_s\,dX_s \Bigr) \Bigm| X_0=x, \,Y_0=y \Bigr] .\]
A short proof of this formula is given, and it is shown how to deduce from it the apparently more general
\[ \mathbb{E}\Bigl[ \exp\Bigr( iu\int_0^1 X_s\,dY_s+iv\int_0^1 Y_s\,dX_s \Bigr) \Bigr] \]
computed by Berthuet.
@incollection {key580140m,
AUTHOR = {Yor, Marc},
TITLE = {Remarques sur une formule de {P}aul
{L}\'evy [Remarks on a formula of {P}aul
{L}\'evy]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {343--346},
DOI = {10.1007/BFb0089501},
URL = {http://www.numdam.org/item?id=SPS_1980__14__343_0},
NOTE = {MR:580140. Zbl:0429.60045.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
C. Cocozza and M. Yor :
“Démonstration d’un théorème de F. Knight à l’aide de martingales exponentielles Demonstration of a theorem of F. Knight using exponential martingales ],
pp. 496–499
in
Séminaire de probabilités XIV
[Fourteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 784 .
Springer (Berlin ),
1980 .
MR
580150 Zbl
0432.60057 incollection
Abstract
People
BibTeX
This is a new proof of Knight’s theorem that (roughly) finitely many orthogonal continuous local martingales, when separately time-changed into Brownian motions, become independent. A similar theorem for the Poisson case is proved in the same way.
@incollection {key580150m,
AUTHOR = {Cocozza, C. and Yor, M.},
TITLE = {D\'emonstration d'un th\'eor\`eme de
{F}. {K}night \`a l'aide de martingales
exponentielles [Demonstration of a theorem
of {F}. {K}night using exponential martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIV}
[Fourteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {784},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
PAGES = {496--499},
DOI = {10.1007/BFb0089511},
URL = {http://www.numdam.org/item?id=SPS_1980__14__496_0},
NOTE = {MR:580150. Zbl:0432.60057.},
ISSN = {0075-8434},
ISBN = {9783540097600},
}
Séminaire de probabilités XV Fifteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 850 .
Springer (Berlin ),
1981 .
With a general index to the papers from the Seminars 1966/67–1978/79.
MR
622550 Zbl
0447.00009 book
People
BibTeX
@book {key622550m,
TITLE = {S\'eminaire de probabilit\'es {XV} [Fifteenth
probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {850},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
PAGES = {iv+704},
DOI = {10.1007/BFb0088355},
URL = {http://www.numdam.org/numdam-bin/browse?id=SPS_1981__15_},
NOTE = {With a general index to the papers from
the Seminars 1966/67--1978/79. MR:622550.
Zbl:0447.00009.},
ISSN = {0075-8434},
ISBN = {9783540106890},
}
T. Jeulin and M. Yor :
“Sur les distributions de certaines fonctionnelles du mouvement brownien On the distribution of certain functionals of Brownian motion ],
pp. 210–226
in
Séminaire de probabilités XV
[Fifteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 850 .
Springer (Berlin ),
1981 .
MR
622565 Zbl
0462.60077 incollection
Abstract
People
BibTeX
This paper gives new proofs and extensions of results due to Knight, concerning occupation times by the process \( (S_t,B_t) \) up to time \( T_a \) , where \( (B_t) \) is Brownian motion, \( T_a \) the hitting time of \( a \) , and \( (S_t) \) is \( \sup_{s\leq t} B_s \) . The method uses enlargement of filtrations, and martingales similar to those of [Azéma and Yor 1979]. Theorem 3.7 is a decomposition of Brownian paths akin to Williams’ decomposition.
@incollection {key622565m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Sur les distributions de certaines fonctionnelles
du mouvement brownien [On the distribution
of certain functionals of {B}rownian
motion]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XV} [Fifteenth
probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {850},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
PAGES = {210--226},
DOI = {10.1007/BFb0088370},
URL = {http://www.numdam.org/item?id=SPS_1981__15__210_0},
NOTE = {MR:622565. Zbl:0462.60077.},
ISSN = {0075-8434},
}
M. Yor :
“Sur certains commutateurs d’une filtration On certain commutators of a filtration ],
pp. 526–528
in
Séminaire de Probabilités XV
[Fifteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 850 .
Springer (Berlin ),
1981 .
MR
622585 Zbl
0456.60057 incollection
Abstract
People
BibTeX
Let \( (\mathcal{F}_t) \) be a filtration satisfying the usual conditions and \( \mathcal{G} \) be a \( \sigma \) -field. Then the conditional expectation \( \mathbb{E}[\,\cdot\mid\mathcal{G}] \) commutes with \( \mathbb{E}[\,\cdot\mid\mathcal{F}_T] \) for all stopping times \( T \) if and only if for some stopping time \( S \) , \( \mathcal{G} \) lies between \( \mathcal{F}_{S-} \) and \( \mathcal{F}_S \) .
@incollection {key622585m,
AUTHOR = {Yor, M.},
TITLE = {Sur certains commutateurs d'une filtration
[On certain commutators of a filtration]},
BOOKTITLE = {S\'eminaire de Probabilit\'es {XV} [Fifteenth
probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {850},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
PAGES = {526--528},
DOI = {10.1007/BFb0088391},
URL = {http://www.numdam.org/item?id=SPS_1981__15__526_0},
NOTE = {MR:622585. Zbl:0456.60057.},
ISSN = {0075-8434},
ISBN = {9783540106890},
}
D. Lépingle, P.-A. Meyer, and M. Yor :
“Extrémalité et remplissage de tribus pour certaines martingales purement discontinues Extremality and the filling of families for certain purely discontinuous martingales ],
pp. 604–617
in
Séminaire de probabilités XV
[Fifteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 850 .
Springer (Berlin ),
1981 .
MR
622591 Zbl
0461.60064 incollection
Abstract
People
BibTeX
This paper consists roughly of two parts. First, the study of a filtration where all martingales are purely discontinuous, and jump on a given well-ordered optional set. Then under a simple separability assumption, one can construct one single martingale which generates the filtration. The second part deals with the same problem as in [Stroock and Yor 1981], but replacing continuous martingales by purely discontinuous martingales with unit jumps, and Brownian motion by a Poisson process. It is shown that the situation is much simpler, purity and extremality being equivalent in this case.
@incollection {key622591m,
AUTHOR = {L\'epingle, D. and Meyer, P.-A. and
Yor, M.},
TITLE = {Extr\'emalit\'e et remplissage de tribus
pour certaines martingales purement
discontinues [Extremality and the filling
of families for certain purely discontinuous
martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XV} [Fifteenth
probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {850},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
PAGES = {604--617},
DOI = {10.1007/BFb0088397},
URL = {http://www.numdam.org/item?id=SPS_1981__15__604_0},
NOTE = {MR:622591. Zbl:0461.60064.},
ISSN = {0075-8434},
ISBN = {9783540106890},
}
Séminaire de probabilités XVI Sixteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 920 .
Springer (Berlin ),
1982 .
MR
658668 Zbl
0471.00023 book
People
BibTeX
@book {key658668m,
TITLE = {S\'eminaire de probabilit\'es {XVI}
[Sixteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {920},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {v+623},
DOI = {10.1007/BFb0092765},
NOTE = {MR:658668. Zbl:0471.00023.},
ISSN = {0075-8434},
ISBN = {9783540114857},
}
N. Falkner, C. Stricker, and M. Yor :
“Temps d’arrêt riches et applications Rich stopping times and applications ],
pp. 213–218
in
Séminaire de probabilités XVI
[Sixteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 920 .
Springer (Berlin ),
1982 .
MR
658683 Zbl
0485.60034 incollection
Abstract
People
BibTeX
This paper starts from the existence of increasing left-continuous processes \( (A_t) \) which generate the previsible \( \sigma \) -field, i.e., every previsible process can be represented as \( f(X_t) \) for some Borel function \( f \) (see [Dellacherie and Stricker 1982]), to prove the existence (discovered by the first named author) of “rich” stopping times \( T \) , i.e., previsible stopping times which encode the whole past up to time
\[ T: \sigma(T)=\mathcal{F}_{T-} \]
(a few details are omitted here). This result leads to counterexamples: a non-reversible semimartingale (see the preceding paper [Walsh 1982]) and a stopping time \( T \) for Brownian motion such that \( L^a_T \) is not a semimartingale in its space variable \( a \) .
@incollection {key658683m,
AUTHOR = {Falkner, N. and Stricker, C. and Yor,
M.},
TITLE = {Temps d'arr\^et riches et applications
[Rich stopping times and applications]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XVI}
[Sixteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {920},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {213--218},
DOI = {10.1007/BFb0092784},
URL = {http://www.numdam.org/item?id=SPS_1982__16__213_0},
NOTE = {MR:658683. Zbl:0485.60034.},
ISSN = {0075-8434},
ISBN = {9783540114857},
}
M. Yor :
“Application de la rélation de domination à certains renforcements des inégalités de martingales Applications of the domination relation for certain strengthenings of martingale inequalities ],
pp. 221–233
in
Séminaire de probabilités XVI
[Sixteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 920 .
Springer (Berlin ),
1982 .
MR
658685 Zbl
0479.60050 incollection
Abstract
People
BibTeX
The domination relation [Lenglart 1977] between a positive, right-continuous process \( X \) and a previsible increasing process \( A \) holds whenever
\[ \mathbb{E}[X_T]\leq \mathbb{E}[A_T] \]
at stopping times. It plays an important role in the paper [1980] of Lenglart–Lepingle–Pratelli on martingale inequalities. Here it is shown to imply a general inequality involving \( X^*_{\infty} \) and \( 1/A_{\infty} \) , from which follow a number of inequalities for a continuous local martingale \( M \) . Among them, estimates on the ratios of the three quantities \( M^*_{\infty} \) , \( \langle M\rangle_{\infty} \) , \( \sup_{a,t} L^a_t \) . One can recover also the stronger version of Doob’s inequality, proved by Pitman [1981].
@incollection {key658685m,
AUTHOR = {Yor, M.},
TITLE = {Application de la r\'elation de domination
\`a certains renforcements des in\'egalit\'es
de martingales [Applications of the
domination relation for certain strengthenings
of martingale inequalities]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XVI}
[Sixteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {920},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {221--233},
DOI = {10.1007/BFb0092786},
URL = {http://www.numdam.org/item?id=SPS_1982__16__221_0},
NOTE = {MR:658685. Zbl:0479.60050.},
ISSN = {0075-8434},
ISBN = {9783540114857},
}
M. Yor :
“Sur la transformée de Hilbert des temps locaux browniens, et une extension de la formule d’Itô On the Hilbert transformation of Brownian local times, and an extension of Itô’s formula ],
pp. 238–247
in
Séminaire de probabilités XVI
[Sixteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 920 .
Springer (Berlin ),
1982 .
MR
658687 Zbl
0495.60080 incollection
Abstract
People
BibTeX
This paper is about the application to the function
\[ (x-a)\log|x-a|-(x-a) \]
(whose second derivative is \( 1/(x-a) \) ) of the Itô–Tanaka formula; the last term then involves a formal Hilbert transform \( \tilde{L^a_t} \) of the local time process \( L^a_t \) . Such processes had been defined by Ito and McKean, and studied by Yamada as examples of Fukushima’s “additive functionals of zero energy”. Here it is proved, as a consequence of a general theorem, that this process has a jointly continuous version — more precisely, Hölder continuous of all orders \( \lt 1/2 \) in \( a \) and in \( t \) .
@incollection {key658687m,
AUTHOR = {Yor, M.},
TITLE = {Sur la transform\'ee de {H}ilbert des
temps locaux browniens, et une extension
de la formule d'{I}t\^o [On the {H}ilbert
transformation of {B}rownian local times,
and an extension of {I}t\^o's formula]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XVI}
[Sixteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {920},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {238--247},
DOI = {10.1007/BFb0092788},
URL = {http://www.numdam.org/item?id=SPS_1982__16__238_0},
NOTE = {MR:658687. Zbl:0495.60080.},
ISSN = {0075-8434},
ISBN = {9783540114857},
}
Séminaire de probabilités XVI: Supplément: Géométrie différentielle stochastique Sixteenth probability seminar: Supplement: Stochastic differential geometry ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 921 .
Springer (Berlin ),
1982 .
MR
658721 Zbl
0471.00024 book
People
BibTeX
@book {key658721m,
TITLE = {S\'eminaire de probabilit\'es {XVI}:
{S}uppl\'ement: {G}\'eom\'etrie diff\'erentielle
stochastique [Sixteenth probability
seminar: {S}upplement: {S}tochastic
differential geometry]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {921},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
PAGES = {i+285},
DOI = {10.1007/BFb0092646},
NOTE = {MR:658721. Zbl:0471.00024.},
ISSN = {0075-8434},
ISBN = {9783540114864},
}
Séminaire de probabilités XVII Seventeenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 986 .
Springer (Berlin ),
1983 .
MR
770391 Zbl
0498.00003 book
People
BibTeX
@book {key770391m,
TITLE = {S\'eminaire de probabilit\'es {XVII}
[Seventeenth probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {986},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1983},
PAGES = {v+512},
DOI = {10.1007/BFb0068294},
NOTE = {MR:770391. Zbl:0498.00003.},
ISSN = {0075-8434},
ISBN = {9783540122890},
}
J.-F. Le Gall and M. Yor :
“Sur l’équation stochastique de Tsirelson On Tsirelson’s stochastic equation ],
pp. 81–88
in
Séminaire de probabilités XVII
[Seventeenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 986 .
Springer (Berlin ),
1983 .
MR
770399 Zbl
0535.60052 incollection
People
BibTeX
@incollection {key770399m,
AUTHOR = {Le Gall, J.-F. and Yor, M.},
TITLE = {Sur l'\'equation stochastique de {T}sirelson
[On {T}sirelson's stochastic equation]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XVII}
[Seventeenth probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {986},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1983},
PAGES = {81--88},
DOI = {10.1007/BFb0068302},
URL = {http://www.numdam.org/item?id=SPS_1983__17__81_0},
NOTE = {MR:770399. Zbl:0535.60052.},
ISSN = {0075-8434},
ISBN = {9783540122890},
}
M. Yor :
“Le drap brownien comme limite en loi de temps locaux linéaires The Brownian sheet as a limit in law of local linear time ],
pp. 89–105
in
Séminaire de probabilités XVII
[Seventeenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 986 .
Springer (Berlin ),
1983 .
MR
770400 Zbl
0514.60075 incollection
Abstract
People
BibTeX
@incollection {key770400m,
AUTHOR = {Yor, Marc},
TITLE = {Le drap brownien comme limite en loi
de temps locaux lin\'eaires [The {B}rownian
sheet as a limit in law of local linear
time]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XVII}
[Seventeenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {986},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1983},
PAGES = {89--105},
DOI = {10.1007/BFb0068303},
URL = {http://www.numdam.org/item?id=SPS_1983__17__89_0},
NOTE = {MR:770400. Zbl:0514.60075.},
ISSN = {0075-8434},
ISBN = {9783540122890},
}
Séminaire de probabilités XVIII Eighteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1059 .
Springer (Berlin ),
1984 .
MR
770944 Zbl
0527.00020 book
People
BibTeX
@book {key770944m,
TITLE = {S\'eminaire de probabilit\'es {XVIII}
[Eighteenth probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1059},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1984},
PAGES = {iv+518},
DOI = {10.1007/BFb0100027},
NOTE = {MR:770944. Zbl:0527.00020.},
ISSN = {0075-8434},
ISBN = {9783540133322},
}
Séminaire de probabilités XIX Nineteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1123 .
Springer (Berlin ),
1985 .
MR
889463 Zbl
0549.00021 book
People
BibTeX
@book {key889463m,
TITLE = {S\'eminaire de probabilit\'es {XIX}
[Nineteenth probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1123},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1985},
PAGES = {iv+504},
DOI = {10.1007/BFb0075834},
NOTE = {MR:889463. Zbl:0549.00021.},
ISSN = {0075-8434},
ISBN = {9783540393979},
}
M. Yor :
“Compléments aux formules de Tanaka–Rosen Complements to the Tanaka–Rosen formulas ],
pp. 332–349
in
Séminaire de probabilités XIX
[Nineteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1123 .
Springer (Berlin ),
1985 .
MR
889493 Zbl
0563.60073 incollection
Abstract
People
BibTeX
Several variants of Rosen’s works [Rosen 1983; 1985; 1986] are presented. They yield Tanaka-type formulae for the self-intersection local times of Brownian motion in dimension 2 and beyond, establishing again Varadhan’s normalization result [Symanzik 1969, Appendix]. The methods involve stochastic calculus, which was not needed in [Le Gall 1985].
@incollection {key889493m,
AUTHOR = {Yor, Marc},
TITLE = {Compl\'ements aux formules de {T}anaka--{R}osen
[Complements to the {T}anaka--{R}osen
formulas]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIX}
[Nineteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1123},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1985},
PAGES = {332--349},
DOI = {10.1007/BFb0075864},
URL = {http://www.numdam.org/item?id=SPS_1985__19__332_0},
NOTE = {MR:889493. Zbl:0563.60073.},
ISSN = {0075-8434},
ISBN = {9783540393979},
}
M. Yor :
“Renormalisation et convergence en loi pour les temps locaux d’intersection du mouvement brownien dans \( \mathbb{R}^3 \) Renormalization and convergence in law for local times of intersection of Brownian motion on \( \mathbb{R}^3 \) ],
pp. 350–365
in
Séminaire de probabilités XIX
[Nineteenth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1123 .
Springer (Berlin ),
1985 .
MR
889494 Zbl
0569.60075 incollection
Abstract
People
BibTeX
It is shown that no renormalization à la Varadhan occurs for the self-intersection local times of 3-dimensional Brownian motion; but a weaker result is established: when the point \( y\in\mathbb{R}^3 \) tends to 0, the self-intersection local time at \( y \) , on the triangle
\[ \{0\lt s\lt u\leq t\},\quad t\geq 0,\]
centered and divided by \( (-\log|y|)^{1/2} \) , converges in law to a Brownian motion. Several variants of this theorem are established.
@incollection {key889494m,
AUTHOR = {Yor, M.},
TITLE = {Renormalisation et convergence en loi
pour les temps locaux d'intersection
du mouvement brownien dans \$\mathbb{R}^3\$
[Renormalization and convergence in
law for local times of intersection
of {B}rownian motion on \$\mathbb{R}^3\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XIX}
[Nineteenth probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1123},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1985},
PAGES = {350--365},
DOI = {10.1007/BFb0075865},
URL = {http://www.numdam.org/item?id=SPS_1985__19__350_0},
NOTE = {MR:889494. Zbl:0569.60075.},
ISSN = {0075-8434},
ISBN = {9783540393979},
}
Séminaire de probabilités XX Twentieth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1204 .
Springer (Berlin ),
1986 .
MR
942008 Zbl
0593.00014 book
People
BibTeX
@book {key942008m,
TITLE = {S\'eminaire de probabilit\'es {XX} [Twentieth
probability seminar]},
EDITOR = {Az\'ema, J. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1204},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1986},
PAGES = {vi+639},
DOI = {10.1007/BFb0075705},
NOTE = {MR:942008. Zbl:0593.00014.},
ISSN = {0075-8434},
ISBN = {9783540167792},
}
M. Yor :
“Sur la représentation comme intégrales stochastiques des temps d’occupation du mouvement Brownien dans \( \mathbb{R}^d \) On the stochastic integral representation of occupation times of Brownian motion in \( \mathbb{R}^d \) ],
pp. 543–552
in
Séminaire de probabilités XX
[Twentieth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1204 .
Springer (Berlin ),
1986 .
MR
942043 Zbl
0611.60067 incollection
Abstract
People
BibTeX
@incollection {key942043m,
AUTHOR = {Yor, Marc},
TITLE = {Sur la repr\'esentation comme int\'egrales
stochastiques des temps d'occupation
du mouvement {B}rownien dans \$\mathbb{R}^d\$
[On the stochastic integral representation
of occupation times of Brownian motion
in \$\mathbb{R}^d\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XX} [Twentieth
probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1204},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1986},
PAGES = {543--552},
DOI = {10.1007/BFb0075740},
URL = {http://www.numdam.org/item?id=SPS_1986__20__543_0},
NOTE = {MR:942043. Zbl:0611.60067.},
ISSN = {0075-8434},
ISBN = {9783540398608},
}
M. Yor :
“Précisions sur l’existence et la continuité des temps locaux d’intersection du mouvement brownien dans \( \mathbb{R}^2 \) Details on the existence and continuity of intersection local times of Brownian motion in \( \mathbb{R}^2 \) ],
pp. 532–542
in
Séminaire de probabilités XX
[Twentieth probability seminar ].
Edited by J. Azéma and M. Yor .
Lecture Notes in Mathematics 1204 .
Springer (Berlin ),
1986 .
MR
942042 Zbl
0611.60066 incollection
People
BibTeX
@incollection {key942042m,
AUTHOR = {Yor, Marc},
TITLE = {Pr\'ecisions sur l'existence et la continuit\'e
des temps locaux d'intersection du mouvement
brownien dans \$\mathbb{R}^2\$ [Details
on the existence and continuity of intersection
local times of Brownian motion in \$\mathbb{R}^2\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XX} [Twentieth
probability seminar]},
EDITOR = {Az\'ema, Jacques and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1204},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1986},
PAGES = {532--542},
DOI = {10.1007/BFb0075739},
URL = {http://www.numdam.org/item?id=SPS_1986__20__532_0},
NOTE = {MR:942042. Zbl:0611.60066.},
ISSN = {0075-8434},
ISBN = {9783540398608},
}
Séminaire de probabilités XXI Twenty-first probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941971 Zbl
0606.00022 book
People
BibTeX
@book {key941971m,
TITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {iv+579},
DOI = {10.1007/BFb0077623},
NOTE = {MR:941971. Zbl:0606.00022.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
S. Song and M. Yor :
“Inégalités pour les processus self-similaires arrêtés à un temps quelconque Inequalities for self-similar processes stopping at an arbitrary time ],
pp. 230–245
in
Séminaire de probabilités XXI
[Twenty-first probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941987 Zbl
0624.60065 incollection
People
BibTeX
@incollection {key941987m,
AUTHOR = {Song, S. and Yor, M.},
TITLE = {In\'egalit\'es pour les processus self-similaires
arr\^et\'es \`a un temps quelconque
[Inequalities for self-similar processes
stopping at an arbitrary time]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {230--245},
DOI = {10.1007/BFb0077638},
URL = {http://www.numdam.org/item?id=SPS_1987__21__230_0},
NOTE = {MR:941987. Zbl:0624.60065.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
J. Azéma and M. Yor :
“Interprétation d’un calcul de H. Tanaka en théorie générale des processus Interpretation of a calculus of H. Tanaka in the general theory of processes ],
pp. 262–269
in
Séminaire de probabilités XXI
[Twenty-first probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941989 Zbl
0621.60085 incollection
People
BibTeX
@incollection {key941989m,
AUTHOR = {Az\'ema, J. and Yor, M.},
TITLE = {Interpr\'etation d'un calcul de {H}.
{T}anaka en th\'eorie g\'en\'erale des
processus [Interpretation of a calculus
of {H}. {T}anaka in the general theory
of processes]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {262--269},
DOI = {10.1007/BFb0077640},
URL = {http://www.numdam.org/item?id=SPS_1987__21__262_0},
NOTE = {MR:941989. Zbl:0621.60085.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
P. Biane, J.-F. Le Gall, and M. Yor :
“Un processus qui ressemble au pont brownien A process that resembles the Brownian bridge ],
pp. 270–275
in
Séminaire de probabilités XXI
[Twenty-first probability seminar ].
Edited by J. Az’e\ma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941990 Zbl
0621.60086 incollection
People
BibTeX
@incollection {key941990m,
AUTHOR = {Biane, Ph. and Le Gall, J.-F. and Yor,
M.},
TITLE = {Un processus qui ressemble au pont brownien
[A process that resembles the {B}rownian
bridge]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az'e\ma, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {270--275},
DOI = {10.1007/BFb0077641},
URL = {http://www.numdam.org/item?id=SPS_1987__21__270_0},
NOTE = {MR:941990. Zbl:0621.60086.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
J. Y. Calais and M. Yor :
“Renormalisation et convergence en loi pour certaines intégrales multiples associées au mouvement brownien dans \( \mathbb{R}^d \) Renormalisation and convergence in law for certain multiple integrals associated with Brownian motion in \( \mathbb{R}^d \) ],
pp. 375–403
in
Séminaire de probabilités XXI
[Twenty-first probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941995 Zbl
0624.60067 incollection
People
BibTeX
@incollection {key941995m,
AUTHOR = {Calais, J. Y. and Yor, M.},
TITLE = {Renormalisation et convergence en loi
pour certaines int\'egrales multiples
associ\'ees au mouvement brownien dans
\$\mathbb{R}^d\$ [Renormalisation and
convergence in law for certain multiple
integrals associated with {B}rownian
motion in \$\mathbb{R}^d\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az\'ema, Jacques and Meyer, Paul Andr\'e
and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {375--403},
DOI = {10.1007/BFb0077646},
URL = {http://www.numdam.org/item?id=SPS_1987__21__375_0},
NOTE = {MR:941995. Zbl:0624.60067.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
Séminaire de probabilités XXII Twenty-second probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1321 .
Springer (Berlin ),
1988 .
MR
960506 Zbl
0635.00013 book
People
BibTeX
@book {key960506m,
TITLE = {S\'eminaire de probabilit\'es {XXII}
[Twenty-second probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1321},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1988},
PAGES = {iv+600},
DOI = {10.1007/BFb0084116},
NOTE = {MR:960506. Zbl:0635.00013.},
ISSN = {0075-8434},
ISBN = {9783540193517},
}
M. Yor :
“Remarques sur certaines constructions des mouvements browniens fractionnaires Remarks on certain constructions of fractional Brownian motions ],
pp. 217–224
in
Séminaire de probabilités XXII
[Twenty-second probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1321 .
Springer (Berlin ),
1988 .
MR
960530 Zbl
0656.60087 incollection
People
BibTeX
@incollection {key960530m,
AUTHOR = {Yor, Marc},
TITLE = {Remarques sur certaines constructions
des mouvements browniens fractionnaires
[Remarks on certain constructions of
fractional {B}rownian motions]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXII}
[Twenty-second probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1321},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1988},
PAGES = {217--224},
DOI = {10.1007/BFb0084140},
URL = {http://www.numdam.org/item?id=SPS_1988__22__217_0},
NOTE = {MR:960530. Zbl:0656.60087.},
ISSN = {0075-8434},
ISBN = {9783540193517},
}
S. Weinryb and M. Yor :
“Le mouvement brownien de Lévy indexé par \( \mathbb{R}^3 \) comme limite centrale de temps locaux d’intersection Lévy Brownian motion for \( \mathbb{R}^3 \) as central limit of intersection local times ],
pp. 225–248
in
Séminaire de probabilités XXII
[Twenty-second probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1321 .
Springer (Berlin ),
1988 .
MR
960531 Zbl
0653.60074 incollection
People
BibTeX
@incollection {key960531m,
AUTHOR = {Weinryb, Sophie and Yor, Marc},
TITLE = {Le mouvement brownien de {L}\'evy index\'e
par \$\mathbb{R}^3\$ comme limite centrale
de temps locaux d'intersection [L\'evy
{B}rownian motion for \$\mathbb{R}^3\$
as central limit of intersection local
times]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXII}
[Twenty-second probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1321},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1988},
PAGES = {225--248},
DOI = {10.1007/BFb0084141},
URL = {http://www.numdam.org/item?id=SPS_1988__22__225_0},
NOTE = {MR:960531. Zbl:0653.60074.},
ISSN = {0075-8434},
ISBN = {9783540193517},
}
P. Biane and M. Yor :
“Sur la loi des temps locaux browniens pris en un temps exponentiel On the law of Brownian local times at an exponential time ],
pp. 454–466
in
Séminaire de probabilités XXII
[Twenty-second probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1321 .
Springer (Berlin ),
1988 .
MR
960541 Zbl
0652.60081 incollection
People
BibTeX
@incollection {key960541m,
AUTHOR = {Biane, Ph. and Yor, M.},
TITLE = {Sur la loi des temps locaux browniens
pris en un temps exponentiel [On the
law of {B}rownian local times at an
exponential time]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXII}
[Twenty-second probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1321},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1988},
PAGES = {454--466},
DOI = {10.1007/BFb0084151},
URL = {http://www.numdam.org/item?id=SPS_1988__22__454_0},
NOTE = {MR:960541. Zbl:0652.60081.},
ISSN = {0075-8434},
ISBN = {9783540193517},
}
Séminaire de probabilités XXIII Twenty-third probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1372 .
Springer (Berlin ),
1989 .
MR
1022893 Zbl
0722.00030 book
People
BibTeX
@book {key1022893m,
TITLE = {S\'eminaire de probabilit\'es {XXIII}
[Twenty-third probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1372},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {iv+583},
DOI = {10.1007/BFb0083955},
NOTE = {MR:1022893. Zbl:0722.00030.},
ISSN = {0075-8434},
ISBN = {9783540511915},
}
J. Azéma and M. Yor :
“Étude d’une martingale remarquable Study of a remarkable martingale ],
pp. 88–130
in
Séminaire de probabilités XXIII
[Twenty-third probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1372 .
Springer (Berlin ),
1989 .
MR
1022900 Zbl
0743.60045 incollection
People
BibTeX
@incollection {key1022900m,
AUTHOR = {Az\'ema, J. and Yor, M.},
TITLE = {\'{E}tude d'une martingale remarquable
[Study of a remarkable martingale]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIII}
[Twenty-third probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1372},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {88--130},
DOI = {10.1007/BFb0083962},
URL = {http://www.numdam.org/item?id=SPS_1989__23__88_0},
NOTE = {MR:1022900. Zbl:0743.60045.},
ISSN = {0075-8434},
ISBN = {9783540511915},
}
M. Barlow, J. Pitman, and M. Yor :
“On Walsh’s Brownian motions 275–293
in
Séminaire de probabilités XXIII
[Twenty-third probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1372 .
Springer (Berlin ),
1989 .
MR
1022917 Zbl
0747.60072 incollection
People
BibTeX
@incollection {key1022917m,
AUTHOR = {Barlow, Martin and Pitman, Jim and Yor,
Marc},
TITLE = {On {W}alsh's {B}rownian motions},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIII}
[Twenty-third probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1372},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {275--293},
DOI = {10.1007/BFb0083979},
URL = {http://www.numdam.org/item?id=SPS_1989__23__275_0},
NOTE = {MR:1022917. Zbl:0747.60072.},
ISSN = {0075-8434},
ISBN = {9783540511915},
}
M. Barlow, J. Pitman, and M. Yor :
“Une extension multidimensionnelle de la loi de l’arc sinus A multidimensional extension of the arcsine law ],
pp. 294–314
in
Séminaire de probabilités XXIII
[Twenty-third probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1372 .
Springer (Berlin ),
1989 .
MR
1022918 Zbl
0738.60072 incollection
People
BibTeX
@incollection {key1022918m,
AUTHOR = {Barlow, Martin and Pitman, Jim and Yor,
Marc},
TITLE = {Une extension multidimensionnelle de
la loi de l'arc sinus [A multidimensional
extension of the arcsine law]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIII}
[Twenty-third probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1372},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {294--314},
DOI = {10.1007/BFb0083980},
URL = {http://www.numdam.org/item?id=SPS_1989__23__294_0},
NOTE = {MR:1022918. Zbl:0738.60072.},
ISSN = {0075-8434},
ISBN = {9783540511915},
}
C. Donati-Martin and M. Yor :
“Mouvement brownien et inégalité de Hardy dans \( L^2 \) Brownian motion and the Hardy inequality on \( L^2 \) ],
pp. 315–323
in
Séminaire de probabilités XXIII
[Twenty-third probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1372 .
Springer (Berlin ),
1989 .
MR
1022919 Zbl
0739.60073 incollection
People
BibTeX
@incollection {key1022919m,
AUTHOR = {Donati-Martin, C. and Yor, M.},
TITLE = {Mouvement brownien et in\'egalit\'e
de {H}ardy dans \$L^2\$ [Brownian motion
and the Hardy inequality on \$L^2\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIII}
[Twenty-third probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1372},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1989},
PAGES = {315--323},
DOI = {10.1007/BFb0083981},
URL = {http://www.numdam.org/item?id=SPS_1989__23__315_0},
NOTE = {MR:1022919. Zbl:0739.60073.},
ISSN = {0075-8434},
ISBN = {9783540511915},
}
Séminaire de probabilités XXIV Twenty-fourth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1426 .
Springer (Berlin ),
1990 .
MR
1071527 Zbl
0695.00024 book
People
BibTeX
@book {key1071527m,
TITLE = {S\'eminaire de probabilit\'es {XXIV}
[Twenty-fourth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1426},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1990},
PAGES = {vi+490},
DOI = {10.1007/BFb0083752},
NOTE = {MR:1071527. Zbl:0695.00024.},
ISSN = {0075-8434},
ISBN = {9783540526940},
}
J. Azéma and M. Yor :
“Dérivation par rapport au processus de Bessel Derivation with respect to a Bessel process ],
pp. 210–226
in
Séminaire de probabilités XXIV
[Twenty-fourth probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1426 .
Springer (Berlin ),
1990 .
MR
1071542 Zbl
0723.60094 incollection
People
BibTeX
@incollection {key1071542m,
AUTHOR = {Az\'ema, J. and Yor, M.},
TITLE = {D\'erivation par rapport au processus
de {B}essel [Derivation with respect
to a {B}essel process]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIV}
[Twenty-fourth probability seminar]},
EDITOR = {Az\'ema, Jacques and Meyer, Paul Andr\'e
and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1426},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1990},
PAGES = {210--226},
DOI = {10.1007/BFb0083767},
URL = {https://eudml.org/doc/113719},
NOTE = {MR:1071542. Zbl:0723.60094.},
ISSN = {0075-8434},
ISBN = {9783540526940},
}
T. Jeulin and M. Yor :
“Filtration des ponts browniens et équations différentielles stochastiques linéaires Filtering of Brownian bridges and linear stochastic differential equations ],
pp. 227–265
in
Séminaire de probabilités XXIV
[Twenty-fourth probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1426 .
Springer (Berlin ),
1990 .
MR
1071543 Zbl
0699.60075 incollection
People
BibTeX
@incollection {key1071543m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Filtration des ponts browniens et \'equations
diff\'erentielles stochastiques lin\'eaires
[Filtering of {B}rownian bridges and
linear stochastic differential equations]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXIV}
[Twenty-fourth probability seminar]},
EDITOR = {Az\'ema, Jacques and Meyer, Paul Andr\'e
and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1426},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1990},
PAGES = {227--265},
DOI = {10.1007/BFb0083768},
URL = {http://www.numdam.org/item?id=SPS_1990__24__227_0},
NOTE = {MR:1071543. Zbl:0699.60075.},
ISSN = {0075-8434},
ISBN = {9783540526940},
}
Séminaire de probabilités XXV Twenty-fifth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1485 .
Springer (Berlin ),
1991 .
MR
1187763 Zbl
0733.00018 book
People
BibTeX
@book {key1187763m,
TITLE = {S\'eminaire de probabilit\'es {XXV}
[Twenty-fifth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1485},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1991},
PAGES = {viii+440},
DOI = {10.1007/BFb0100839},
NOTE = {MR:1187763. Zbl:0733.00018.},
ISSN = {0075-8434},
ISBN = {9783540546160},
}
L. E. Dubins, M. Émery, and M. Yor :
“A continuous martingale in the plane that may spiral away to infinity 284–290
in
Séminaire de probabilités XXV
[Twenty-fifth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1485 .
Springer (Berlin ),
1991 .
MR
1187786 Zbl
0737.60036 incollection
Abstract
People
BibTeX
If \( Z_t=\rho_t e^{i\theta_t} \) is a continuous, complex-valued martingale, is it possible that, with positive probability, both \( \rho_t \) and \( \theta_t \) tend to infinity when \( t\to\infty \) ? If \( Z \) is a conformal martingale, the answer is clearly no (for both \( \log \rho_t \) and \( \theta_t \) are local martingales too). But if conformality is not required, such a behavior is possible. This note gives an example of a planar spiral curve \( \sigma \) and a continuous martingale that never hits \( \sigma \) but still has a non-zero probability of escaping to infinity.
@incollection {key1187786m,
AUTHOR = {Dubins, L. E. and \'Emery, Michel and
Yor, M.},
TITLE = {A continuous martingale in the plane
that may spiral away to infinity},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXV}
[Twenty-fifth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1485},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1991},
PAGES = {284--290},
DOI = {10.1007/BFb0100862},
URL = {http://www.numdam.org/item?id=SPS_1991__25__284_0},
NOTE = {MR:1187786. Zbl:0737.60036.},
ISSN = {0075-8434},
ISBN = {9783540546160},
}
Séminaire de probabilités XXVI Twenty-sixth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1526 .
Springer (Berlin ),
1992 .
MR
1231978 Zbl
0754.00008 book
People
BibTeX
@book {key1231978m,
TITLE = {S\'eminaire de probabilit\'es {XXVI}
[Twenty-sixth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1526},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {x+633},
DOI = {10.1007/BFb0084305},
NOTE = {MR:1231978. Zbl:0754.00008.},
ISSN = {0075-8434},
ISBN = {9783540560210},
}
J. Azéma and M. Yor :
“Sur les zéros des martingales continues On the zeros of continuous martingales ],
pp. 248–306
in
Séminaire de probabilités XXVI
[Twenty-sixth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1526 .
Springer (Berlin ),
1992 .
MR
1231999 Zbl
0765.60038 incollection
People
BibTeX
@incollection {key1231999m,
AUTHOR = {Az\'ema, J. and Yor, M.},
TITLE = {Sur les z\'eros des martingales continues
[On the zeros of continuous martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVI}
[Twenty-sixth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1526},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {248--306},
DOI = {10.1007/BFb0084326},
URL = {http://www.numdam.org/item?id=SPS_1992__26__248_0},
NOTE = {MR:1231999. Zbl:0765.60038.},
ISSN = {0075-8434},
ISBN = {9783540560210},
}
J. Azéma, P.-A. Meyer, and M. Yor :
“Martingales relatives Relative martingales ],
pp. 307–321
in
Séminaire de probabilités XXVI
[Twenty-sixth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1526 .
Springer (Berlin ),
1992 .
MR
1232000 Zbl
0765.60037 incollection
People
BibTeX
@incollection {key1232000m,
AUTHOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
TITLE = {Martingales relatives [Relative martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVI}
[Twenty-sixth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1526},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {307--321},
DOI = {10.1007/BFb0084327},
URL = {http://www.numdam.org/item?id=SPS_1992__26__307_0},
NOTE = {MR:1232000. Zbl:0765.60037.},
ISSN = {0075-8434},
ISBN = {9783540560210},
}
T. Jeulin and M. Yor :
“Une décomposition non-canonique du drap brownien A non-canonical decomposition of the Brownian sheet ],
pp. 322–347
in
Séminaire de probabilités XXVI
[Twenty-sixth seminar on probability ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1526 .
Springer (Berlin ),
1992 .
MR
1232001 Zbl
0767.60082 incollection
Abstract
People
BibTeX
@incollection {key1232001m,
AUTHOR = {Jeulin, Th. and Yor, M.},
TITLE = {Une d\'ecomposition non-canonique du
drap brownien [A non-canonical decomposition
of the {B}rownian sheet]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVI}
[Twenty-sixth seminar on probability]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1526},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {322--347},
DOI = {10.1007/BFb0084328},
URL = {http://www.numdam.org/item?id=SPS_1992__26__322_0},
NOTE = {MR:1232001. Zbl:0767.60082.},
ISSN = {0075-8434},
ISBN = {9783540560210},
}
Séminaire de probabilités XXVII Twenty-seventh probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1557 .
Springer (Berlin ),
1993 .
MR
1308545 Zbl
0780.00013 book
People
BibTeX
@book {key1308545m,
TITLE = {S\'eminaire de probabilit\'es {XXVII}
[Twenty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1557},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {vi+327},
DOI = {10.1007/BFb0087956},
NOTE = {MR:1308545. Zbl:0780.00013.},
ISSN = {0075-8434},
ISBN = {9783540572824},
}
T. Jeulin and M. Yor :
“Moyennes mobiles et semimartingales Moving averages and semimartingales ],
pp. 53–77
in
Séminaire de probabilités XXVII
[Twenty-seventh probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1557 .
Springer (Berlin ),
1993 .
MR
1308553 Zbl
0788.60059 incollection
People
BibTeX
@incollection {key1308553m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Moyennes mobiles et semimartingales
[Moving averages and semimartingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVII}
[Twenty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1557},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {53--77},
DOI = {10.1007/BFb0087964},
URL = {http://www.numdam.org/item?id=SPS_1993__27__53_0},
NOTE = {MR:1308553. Zbl:0788.60059.},
ISSN = {0075-8434},
ISBN = {9783540572824},
}
L. E. Dubins, M. Émery, and M. Yor :
“On the Lévy transformation of Brownian motions and continuous martingales 122–132
in
Séminaire de probabilités XXVII
[Twenty-seventh probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1557 .
Springer (Berlin ),
1993 .
A correction was published in Séminaire de probabilités XLIV (2012)
MR
1308559 Zbl
0844.60055 incollection
People
BibTeX
@incollection {key1308559m,
AUTHOR = {Dubins, L. E. and \'Emery, Michel and
Yor, M.},
TITLE = {On the {L}\'evy transformation of {B}rownian
motions and continuous martingales},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVII}
[Twenty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1557},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {122--132},
DOI = {10.1007/BFb0087970},
URL = {http://www.numdam.org/item?id=SPS_1993__27__122_0},
NOTE = {A correction was published in \textit{S\'eminaire
de probabilit\'es XLIV} (2012). MR:1308559.
Zbl:0844.60055.},
ISSN = {0075-8434},
ISBN = {9783540572824},
}
J. Azéma, T. Jeulin, F. Knight, and M. Yor :
“Le théorème d’arrêt en une fin d’ensemble prévisible The stopping time theorem of a predictable set ],
pp. 133–158
in
Séminaire de probabilités XXVII
[Twenty-seventh probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1557 .
Springer (Berlin ),
1993 .
MR
1308560 Zbl
0798.60048 incollection
People
BibTeX
@incollection {key1308560m,
AUTHOR = {Az\'ema, J. and Jeulin, T. and Knight,
F. and Yor, M.},
TITLE = {Le th\'eor\`eme d'arr\^et en une fin
d'ensemble pr\'evisible [The stopping
time theorem of a predictable set]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVII}
[Twenty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1557},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {133--158},
DOI = {10.1007/BFb0087971},
URL = {http://www.numdam.org/item?id=SPS_1993__27__133_0},
NOTE = {MR:1308560. Zbl:0798.60048.},
ISSN = {0075-8434},
ISBN = {9783540572824},
}
K. D. Elworthy and M. Yor :
“Conditional expectations for derivatives of certain stochastic flows 159–172
in
Séminaire de probabilités XXVII
[Twenty-seventh probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1557 .
Springer (Berlin ),
1993 .
MR
1308561 Zbl
0795.60046 incollection
People
BibTeX
@incollection {key1308561m,
AUTHOR = {Elworthy, K. D. and Yor, M.},
TITLE = {Conditional expectations for derivatives
of certain stochastic flows},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXVII}
[Twenty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1557},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1993},
PAGES = {159--172},
DOI = {10.1007/BFb0087972},
URL = {http://www.numdam.org/item?id=SPS_1993__27__159_0},
NOTE = {MR:1308561. Zbl:0795.60046.},
ISSN = {0075-8434},
ISBN = {9783540572824},
}
Séminaire de probabilités XXVIII Twenty-eighth probability seminar ].
Edited by J. Azéma, P.-A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1583 .
Springer (Berlin ),
1994 .
MR
1329096 Zbl
0797.00020 book
People
BibTeX
@book {key1329096m,
TITLE = {S\'eminaire de probabilit\'es {XXVIII}
[Twenty-eighth probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P.-A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1583},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1994},
PAGES = {vi+334},
DOI = {10.1007/BFb0073829},
NOTE = {MR:1329096. Zbl:0797.00020.},
ISSN = {0075-8434},
ISBN = {9783540583318},
}
Séminaire de probabilités XXIX Twenty-ninth probability seminar ].
Edited by J. Azéma, M. Emery, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1613 .
Springer (Berlin ),
1995 .
MR
1459442 Zbl
0826.00027 book
People
BibTeX
@book {key1459442m,
TITLE = {S\'eminaire de probabilit\'es {XXIX}
[Twenty-ninth probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Meyer,
P. A. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1613},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1995},
PAGES = {vi+326},
DOI = {10.1007/BFb0094193},
NOTE = {MR:1459442. Zbl:0826.00027.},
ISSN = {0075-8434},
ISBN = {9783540602194},
}
Séminaire de probabilités XXX Thirtieth probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1626 .
Springer (Berlin ),
1996 .
MR
1459471 Zbl
0840.00041 book
People
BibTeX
@book {key1459471m,
TITLE = {S\'eminaire de probabilit\'es {XXX}
[Thirtieth probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1626},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1996},
PAGES = {viii+382},
DOI = {10.1007/BFb0094636},
NOTE = {MR:1459471. Zbl:0840.00041.},
ISSN = {0075-8434},
ISBN = {9783540613367},
}
J. Azéma, C. Rainer, and M. Yor :
“Une propriété des martingales pures A property of pure martingales ],
pp. 243–254
in
Séminaire de probabilités XXX
[Thirtieth probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1626 .
Springer (Berlin ),
1996 .
MR
1459487 Zbl
0857.60076 incollection
People
BibTeX
@incollection {key1459487m,
AUTHOR = {Az\'ema, J. and Rainer, C. and Yor,
M.},
TITLE = {Une propri\'et\'e des martingales pures
[A property of pure martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXX}
[Thirtieth probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1626},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1996},
PAGES = {243--254},
DOI = {10.1007/BFb0094652},
URL = {http://www.numdam.org/item?id=SPS_1996__30__243_0},
NOTE = {MR:1459487. Zbl:0857.60076.},
ISSN = {0075-8434},
ISBN = {9783540613367},
}
J. Azéma, T. Jeulin, F. Knight, G. Mokobodzki, and M. Yor :
“Sur les processus croissants de type injectif On growing processes which are injective ],
pp. 312–343
in
Séminaire de probabilités XXX
[Thirtieth probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1626 .
Springer (Berlin ),
1996 .
MR
1459491 Zbl
0859.60035 incollection
People
BibTeX
@incollection {key1459491m,
AUTHOR = {Az\'ema, J. and Jeulin, T. and Knight,
F. and Mokobodzki, G. and Yor, M.},
TITLE = {Sur les processus croissants de type
injectif [On growing processes which
are injective]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXX}
[Thirtieth probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1626},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1996},
PAGES = {312--343},
DOI = {10.1007/BFb0094656},
URL = {http://www.numdam.org/item?id=SPS_1996__30__312_0},
NOTE = {MR:1459491. Zbl:0859.60035.},
ISSN = {0075-8434},
ISBN = {9783540613367},
}
Séminaire de probabilités XXX Thirtieth probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1626 .
Springer (Berlin ),
1996 .
MR
1478710 Zbl
0864.00069 book
People
BibTeX
@book {key1478710m,
TITLE = {S\'eminaire de probabilit\'es {XXX}
[Thirtieth probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1626},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1996},
PAGES = {viii+329},
DOI = {10.1007/BFb0119286},
URL = {http://www.numdam.org/numdam-bin/browse?id=SPS_1997__31_},
NOTE = {MR:1478710. Zbl:0864.00069.},
ISSN = {0075-8434},
ISBN = {9783540613367},
}
K. D. Elworthy, X. M. Li, and M. Yor :
“On the tails of the supremum and the quadratic variation of strictly local martingales 113–125
in
Séminaire de probabilités XXXI
[Thirty-first probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1655 .
Springer (Berlin ),
1997 .
MR
1478722 Zbl
0886.60035 incollection
Abstract
People
BibTeX
The asymptotic tails of the current maximum and the quadratic variation of a positive continuous local martingale are compared. Applications to strict local martingales associated with transient diffusions, such as Bessel processes, and remarkable identities for Bessel functions are given.
@incollection {key1478722m,
AUTHOR = {Elworthy, K. D. and Li, X. M. and Yor,
M.},
TITLE = {On the tails of the supremum and the
quadratic variation of strictly local
martingales},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXI}
[Thirty-first probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1655},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1997},
PAGES = {113--125},
DOI = {10.1007/BFb0119298},
URL = {http://www.numdam.org/item?id=SPS_1997__31__113_0},
NOTE = {MR:1478722. Zbl:0886.60035.},
ISSN = {0075-8434},
ISBN = {9783540626343},
}
J. Pitman and M. Yor :
“On the lengths of excursions of some Markov processes 272–286
in
Séminaire de probabilités XXXI
[Thirty-first probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1655 .
Springer (Berlin ),
1997 .
MR
1478737 Zbl
0884.60071 incollection
Abstract
People
BibTeX
Results are obtained regarding the distribution of the ranked lengths of component intervals in the complement of the random set of times when a recurrent Markov process returns to its starting point. Various martingales are described in terms of the Lévy measure of the Poisson point process of interval lengths on the local time scale. The martingales derived from the zero set of a one-dimensional diffusion are related to martingales studied by Azéma and Rainer. Formulae are obtained which show how the distribution of interval lengths is affected when the underlying process is subjected to a Girsanov transoformation. In particular, results for the zero set of an Ornstein–Uhlenbeck process or a Cox–Ingersoll–Ross process are derived from results for a Brownian motion or recurrent Bessel process, when the zero set is the range of a stable subordinator.
@incollection {key1478737m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {On the lengths of excursions of some
{M}arkov processes},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXI}
[Thirty-first probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1655},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1997},
PAGES = {272--286},
DOI = {10.1007/BFb0119313},
URL = {http://www.numdam.org/item?id=SPS_1997__31__272_0},
NOTE = {MR:1478737. Zbl:0884.60071.},
ISSN = {0075-8434},
ISBN = {9783540626343},
}
J. Pitman and M. Yor :
“On the relative lengths of excursions derived from a stable subordinator 287–305
in
Séminaire de probabilités XXXI
[Thirty-first probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1655 .
Springer (Berlin ),
1997 .
MR
1478738 Zbl
0884.60072 incollection
People
BibTeX
@incollection {key1478738m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {On the relative lengths of excursions
derived from a stable subordinator},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXI}
[Thirty-first probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1655},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1997},
PAGES = {287--305},
DOI = {Results are obtained concerning the
distribution of ranked relative lengths
of excursions of a recurrent Markov
process from a point in its state space
whose inverse local time process is
a stable subordinator. It is shown that
for a large class of random times \$T\$
the distribution of relative excursion
lengths prior to \$T\$ is the same as
if \$T\$ were a fixed time. It follows
that the generalized arc-sine laws of
Lamperti extend to such random times
\$T\$. For some other random times \$T\$,
absolute continuity relations are obtained
which relate the law of the relative
lengths at time \$T\$ to the law at a
fixed time.},
URL = {http://www.numdam.org/item?id=SPS_1997__31__287_0},
NOTE = {MR:1478738. Zbl:0884.60072.},
ISSN = {0075-8434},
ISBN = {9783540626343},
}
M. Yor :
“Some remarks about the joint law of Brownian motion and its supremum 306–314
in
Séminaire de probabilités XXXI
[Thirty-first probability seminar ].
Edited by J. Azéma, M. Emery, and M. Yor .
Lecture Notes in Mathematics 1655 .
Springer (Berlin ),
1997 .
MR
1478739 Zbl
0885.60071 incollection
Abstract
People
BibTeX
Seshadri’s identity says that if \( S_1 \) denotes the maximum of a Brownian motion \( B \) on the interval \( [0,1] \) , the r.v.
\[ 2S_1(S_1-B_1)\]
is independent of \( B_1 \) and exponentially distributed. Several variants of this are obtained.
@incollection {key1478739m,
AUTHOR = {Yor, Marc},
TITLE = {Some remarks about the joint law of
{B}rownian motion and its supremum},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXI}
[Thirty-first probability seminar]},
EDITOR = {Az\'ema, J. and Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1655},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1997},
PAGES = {306--314},
DOI = {10.1007/BFb0119315},
URL = {http://www.numdam.org/item?id=SPS_1997__31__306_0},
NOTE = {MR:1478739. Zbl:0885.60071.},
ISSN = {0075-8434},
ISBN = {9783540626343},
}
Séminaire de probabilités XXXII Thirty-second probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1651223 Zbl
0893.00035 book
People
BibTeX
@book {key1651223m,
TITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {vi+429},
DOI = {10.1007/BFb0101744},
NOTE = {MR:1651223. Zbl:0893.00035.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
R. A. Doney, J. Warren, and M. Yor :
“Perturbed Bessel processes 237–249
in
Séminaire de probabilités XXXII
[Thirty-second probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1655297 Zbl
0924.60039 incollection
Abstract
People
BibTeX
There has been some interest in the literature in Brownian motion perturbed at its maximum; that is a process \( (X_t \) ; \( t\geq 0) \) satisfying
\[ X_t = B_t + \alpha M_t^X, \]
where
\[ M_t^X = \sup_{0\leq s\leq t} X_s ,\]
and \( (B_t \) ; \( t\geq 0) \) is Brownian motion issuing from zero. The parameter \( \alpha \) must satisfy \( \alpha \lt 1 \) . For example arc-sine laws and Ray–Knight theorems have been obtained for this process; see [Carmona et al. 1994; Werner 1995; Doney 1998]. Our initial aim was to identify a process which could be considered as the process \( X \) conditioned to stay positive. This new process behaves like the Bessel process of dimension three except when at its maximum and we call it a perturbed three-dimensional Bessel process. We establish Ray–Knight theorems for the local times of this process, up to a first passage time and up to infinity, and observe that these descriptions coincide with those of the local times of two processes that have been considered in [Yor 1992]. We give an explanation for this coincidence by showing that these processes are linked to the perturbed three dimensional Bessel process by space-time transformations and time-reversal.
@incollection {key1655297m,
AUTHOR = {Doney, R. A. and Warren, J. and Yor,
M.},
TITLE = {Perturbed {B}essel processes},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {237--249},
DOI = {10.1007/BFb0101761},
URL = {http://www.numdam.org/item?id=SPS_1998__32__237_0},
NOTE = {MR:1655297. Zbl:0924.60039.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
M. T. Barlow, M. Émery, F. B. Knight, S. Song, and M. Yor :
“Autour d’un théorème de Tsirelson sur des filtrations browniennes et non browniennes On a theorem of Tsirelson concerning Brownian and non-Brownian filtrations ],
pp. 264–305
in
Séminaire de probabilités XXXII
[Thirty-second probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1655299 Zbl
0914.60064 incollection
Abstract
People
BibTeX
Tsirelson has shown that no Walsh’s Brownian motion with three rays or more can live in a Brownian filtration [1997]. Using his methods, the result is extended to spider martingales. A conjecture of M. Barlow is also proved: if \( L \) is an honest time in a (possibly multidimensional) Brownian filtration, then \( \mathcal{F}_{L+} \) is generated by \( \mathcal{F}_L \) and at most one event. Last, it is shown that a Walsh’s Brownian motion can live in the filtration generated by another Walsh’s Brownian motion only if the former is obtained from the latter by aggregating rays.
@incollection {key1655299m,
AUTHOR = {Barlow, M. T. and \'Emery, M. and Knight,
F. B. and Song, S. and Yor, M.},
TITLE = {Autour d'un th\'eor\`eme de {T}sirelson
sur des filtrations browniennes et non
browniennes [On a theorem of {T}sirelson
concerning {B}rownian and non-{B}rownian
filtrations]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {264--305},
DOI = {10.1007/BFb0101763},
URL = {http://www.numdam.org/item?id=SPS_1998__32__264_0},
NOTE = {MR:1655299. Zbl:0914.60064.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
M. Émery and M. Yor :
“Sur un théorème de Tsirelson relatif à des mouvements browniens corrélés et à la nullité de certains temps locaux On a theorem of Tsirelson with respect to correlated Brownian motion and the nullity of certain local times ],
pp. 306–312
in
Séminaire de probabilités XXXII
[Thirty-second probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1655300 Zbl
0949.60088 incollection
People
BibTeX
@incollection {key1655300m,
AUTHOR = {\'Emery, M. and Yor, M.},
TITLE = {Sur un th\'eor\`eme de {T}sirelson relatif
\`a des mouvements browniens corr\'el\'es
et \`a la nullit\'e de certains temps
locaux [On a theorem of {T}sirelson
with respect to correlated {B}rownian
motion and the nullity of certain local
times]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {306--312},
DOI = {10.1007/BFb0101764},
URL = {http://www.numdam.org/item?id=SPS_1998__32__306_0},
NOTE = {MR:1655300. Zbl:0949.60088.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
J. Azéma, T. Jeulin, F. Knight, and M. Yor :
“Quelques calculs de compensateurs impliquant l’injectivité de certains processus croissants Some computations including the injectivity of certain increasing processes ],
pp. 316–327
in
Séminaire de probabilités XXXII
[Thirty-second probability seminar ],
vol. 1686 .
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1655302 Zbl
0915.60058 incollection
People
BibTeX
@incollection {key1655302m,
AUTHOR = {Az\'ema, J. and Jeulin, T. and Knight,
F. and Yor, M.},
TITLE = {Quelques calculs de compensateurs impliquant
l'injectivit\'e de certains processus
croissants [Some computations including
the injectivity of certain increasing
processes]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
VOLUME = {1686},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {316--327},
DOI = {10.1007/BFb0101766},
URL = {http://www.numdam.org/item?id=SPS_1998__32__316_0},
NOTE = {MR:1655302. Zbl:0915.60058.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
J. Warren and M. Yor :
“The Brownian burglar: Conditioning Brownian motion by its local time process 328–342
in
Séminaire de probabilités XXXII
[Thirty-second probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1686 .
Springer (Berlin ),
1998 .
MR
1655303 Zbl
0924.60072 incollection
People
BibTeX
@incollection {key1655303m,
AUTHOR = {Warren, J. and Yor, M.},
TITLE = {The {B}rownian burglar: {C}onditioning
{B}rownian motion by its local time
process},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXII}
[Thirty-second probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1686},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1998},
PAGES = {328--342},
DOI = {10.1007/BFb0101767},
URL = {http://www.numdam.org/item?id=SPS_1998__32__328_0},
NOTE = {MR:1655303. Zbl:0924.60072.},
ISSN = {0075-8434},
ISBN = {9783540643760},
}
Séminaire de probabilités XXXIII Thirty-third probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1709 .
Springer (Berlin ),
1999 .
MR
1768019 Zbl
0924.00016 book
People
BibTeX
@book {key1768019m,
TITLE = {S\'eminaire de probabilit\'es {XXXIII}
[Thirty-third probability seminar]},
EDITOR = {Az\'ema, Jacques and \'Emery, Michel
and Ledoux, Michel and Yor, Marc},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1709},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1999},
PAGES = {viii+418},
DOI = {10.1007/BFb0096508},
NOTE = {MR:1768019. Zbl:0924.00016.},
ISSN = {0075-8434},
ISBN = {9783540663423},
}
L. Vostrikova and M. Yor :
“Some invariance properties (of the laws) of Ocone’s martingales 417–431
in
Séminaire de probabilités XXXIV
[Thirty-fourth probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1729 .
Springer (Berlin ),
2000 .
MR
1768078 Zbl
0965.60047 incollection
People
BibTeX
@incollection {key1768078m,
AUTHOR = {Vostrikova, L. and Yor, M.},
TITLE = {Some invariance properties (of the laws)
of {O}cone's martingales},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXIV}
[Thirty-fourth probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1729},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2000},
PAGES = {417--431},
DOI = {10.1007/BFb0103817},
URL = {http://www.numdam.org/item?id=SPS_2000__34__417_0},
NOTE = {MR:1768078. Zbl:0965.60047.},
ISSN = {0075-8434},
ISBN = {9783540673149},
}
Séminaire de probabilités XXXIV Thirty-fourth probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1729 .
Springer (Berlin ),
2000 .
MR
1768089 Zbl
0940.00007 book
People
BibTeX
@book {key1768089m,
TITLE = {S\'eminaire de probabilit\'es {XXXIV}
[Thirty-fourth probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1729},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2000},
PAGES = {vi+431},
DOI = {10.1007/BFb0103797},
NOTE = {MR:1768089. Zbl:0940.00007.},
ISSN = {0075-8434},
ISBN = {9783540673149},
}
Séminaire de probabilités XXXV Thirty-fifth probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1755 .
Springer (Berlin ),
2001 .
MR
1837273 Zbl
0960.00020 book
People
BibTeX
@book {key1837273m,
TITLE = {S\'eminaire de probabilit\'es {XXXV}
[Thirty-fifth probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1755},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2001},
PAGES = {vi+427},
DOI = {10.1007/b76885},
NOTE = {MR:1837273. Zbl:0960.00020.},
ISSN = {0075-8434},
ISBN = {9783540416593},
}
L. Chaumont, D. G. Hobson, and M. Yor :
“Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes 334–347
in
Séminaire de probabilités XXXV
[Thirty-fifth probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1755 .
Springer (Berlin ),
2001 .
MR
1837296 Zbl
0982.60020 incollection
Abstract
People
BibTeX
In this paper we derive some distributional properties of Lévy processes and bridges from their cyclic exchangeability property. We first describe the \( \sigma \) -field which is invariant under the cyclic transformations. Then, by comditioning on this \( \sigma \) -field, we obtain some information about the laws of many functionals of Lévy processes and bridges, such as exponential functionals, quantiles and local time.
@incollection {key1837296m,
AUTHOR = {Chaumont, L. and Hobson, D. G. and Yor,
M.},
TITLE = {Some consequences of the cyclic exchangeability
property for exponential functionals
of {L}\'evy processes},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXXV}
[Thirty-fifth probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1755},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2001},
PAGES = {334--347},
DOI = {10.1007/978-3-540-44671-2_23},
URL = {http://www.numdam.org/item?id=SPS_2001__35__334_0},
NOTE = {MR:1837296. Zbl:0982.60020.},
ISSN = {0075-8434},
ISBN = {9783540416593},
}
Séminaire de probabilités XXXVI Thirty-sixth seminar on probability ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1801 .
Springer (Berlin ),
2003 .
MR
1971581 Zbl
1003.00010 book
People
BibTeX
@book {key1971581m,
TITLE = {S\'eminaire de probabilit\'es {XXXVI}
[Thirty-sixth seminar on probability]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1801},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2003},
PAGES = {viii+497},
DOI = {10.1007/b10068},
NOTE = {MR:1971581. Zbl:1003.00010.},
ISSN = {0075-8434},
ISBN = {9783540000723},
}
Séminaire de probabilités XXXVII Thirty-seventh probability seminar ].
Edited by J. Azéma, M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1832 .
Springer (Berlin ),
2003 .
MR
2053038 Zbl
1027.00025 book
People
BibTeX
@book {key2053038m,
TITLE = {S\'eminaire de probabilit\'es {XXXVII}
[Thirty-seventh probability seminar]},
EDITOR = {Az\'ema, J. and \'Emery, M. and Ledoux,
M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1832},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2003},
PAGES = {xiv+446},
DOI = {10.1007/b94376},
NOTE = {MR:2053038. Zbl:1027.00025.},
ISSN = {0075-8434},
ISBN = {9783540205203},
}
Séminaire de probabilités XXXVIII Thirty-eighth probability seminar ].
Edited by M. Émery, M. Ledoux, and M. Yor .
Lecture Notes in Mathematics 1857 .
Springer (Berlin ),
2005 .
Dedicated to Jacques Azéma on the occasion on his 65th birthday.
MR
2126961 Zbl
1055.60001 book
People
BibTeX
@book {key2126961m,
TITLE = {S\'eminaire de probabilit\'es {XXXVIII}
[Thirty-eighth probability seminar]},
EDITOR = {\'Emery, M. and Ledoux, M. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1857},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2005},
PAGES = {x+392},
DOI = {10.1007/b104072},
NOTE = {Dedicated to Jacques Az\'ema on the
occasion on his 65th birthday. MR:2126961.
Zbl:1055.60001.},
ISSN = {0075-8434},
ISBN = {9783540239734},
}
J. Azéma, P. Barrieu, J. Bertoin, M. E. Caballero, C. Donati-Martin, M. Émery, F. Hirsch, Y. Hu, M. Ledoux, J. Najnudel, R. Mansuy, L. Miclo, Z. Shi, and D. Williams :
“Témoignages ”
[Testimonials ],
pp. xi–xxx
in
In memoriam Marc Yor: Séminaire de probabilités XLVII
[In memoriam Marc Yor: Forty-seventh probability seminar ].
Edited by C. Donati-Martin, A. Lejay, and A. Rouault .
Lecture Notes in Mathematics 2137 .
Springer (Cham, Switzerland ),
2015 .
MR
3444289 incollection
People
BibTeX
@incollection {key3444289m,
AUTHOR = {Az\'ema, Jacques and Barrieu, Pauline
and Bertoin, Jean and Caballero, Maria
Emilia and Donati-Martin, Catherine
and \'Emery, Michel and Hirsch, Francis
and Hu, Yueyun and Ledoux, Michel and
Najnudel, Joseph and Mansuy, Roger and
Miclo, Laurent and Shi, Zhan and Williams,
David},
TITLE = {T\'emoignages [Testimonials]},
BOOKTITLE = {In memoriam {M}arc {Y}or: {S}\'eminaire
de probabilit\'es {XLVII} [In memoriam
{M}arc {Y}or: {F}orty-seventh probability
seminar]},
EDITOR = {Donati-Martin, Catherine and Lejay,
Antoine and Rouault, Alain},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {2137},
PUBLISHER = {Springer},
ADDRESS = {Cham, Switzerland},
YEAR = {2015},
PAGES = {xi--xxx},
NOTE = {MR:3444289.},
ISSN = {0075-8434},
ISBN = {9783319185842},
}
