M. Yor and P. A. Meyer :
“Sur la théorie de la prédiction, et le problème de décomposition des tribus \( \mathfrak{F}^{\circ}_{t^+} \) On the theory of prediction, and the problem of family decomposition \( \mathfrak{F}^{\circ}_{t^+} \) ],
pp. 104–117
in
Séminaire de probabilités X
[Tenth probability seminar ].
Edited by P. A. Meyer .
Lecture Notes in Mathematics 511 .
Springer (Berlin ),
1976 .
MR
438462 Zbl
0332.60025 incollection
Abstract
People
BibTeX
This paper contains another version of Knight’s theory[Meyer 1976] for càdlàg process instead of measurable processes. These results then are applied to the pathology of germ fields: a natural measurability conjecture does not hold, and an example is given of a process \( X_t \) such that its natural \( \sigma \) -field \( \mathcal{F}_{1+} \) is not generated by \( \mathcal{F}_{1} \) and the germ-field at 0 of the process \( (X_{1+s}) \) .
@incollection {key438462m,
AUTHOR = {Yor, Marc and Meyer, P. A.},
TITLE = {Sur la th\'eorie de la pr\'ediction,
et le probl\`eme de d\'ecomposition
des tribus \$\mathfrak{F}^{\circ}_{t^+}\$
[On the theory of prediction, and the
problem of family decomposition \$\mathfrak{F}^{\circ}_{t^+}\$]},
BOOKTITLE = {S\'eminaire de probabilit\'es {X} [Tenth
probability seminar]},
EDITOR = {Meyer, P. A.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {511},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1976},
PAGES = {104--117},
DOI = {10.1007/BFb0101099},
URL = {http://www.numdam.org/item?id=SPS_1976__10__104_0},
NOTE = {MR:438462. Zbl:0332.60025.},
ISSN = {0075-8434},
ISBN = {9783540076810},
}
M. Yor :
“Sur les intégrales stochastiques optionnelles et une suite remarquable de formules exponentielles On optional stochastic integrals and a remarkable series of exponential formulas ],
pp. 481–500
in
Séminaire de probabilités X
[Tenth probability seminar ].
Edited by P. A. Meyer .
Lecture Notes in Mathematics 511 .
Springer (Berlin ),
1976 .
MR
440699 Zbl
0393.60057 incollection
Abstract
People
BibTeX
This paper contains several useful results on optional stochastic integrals of local martingales and semimartingales, as well as the first occurence of the well-known formula
\[ \mathcal{E}(X)\,\mathcal{E}(Y)=\mathcal{E}(X+Y+[X,Y]) \]
where \( \mathcal{E} \) denotes the usual exponential of semimartingales. Also, the s.d.e.
\[ Z_t=1+\int_0^t Z_s\,dX_s \]
is solved, where \( X \) is a suitable semimartingale, and the integral is an optional one. The Lévy measure of a local martingale is studied, and used to rewrite the Ito formula in a form that involves optional integrals. Finally, a whole family of “exponentials” is introduced, interpolating between the standard one and an exponential involving the Lévy measure, which was used by Kunita–Watanabe in a Markovian set-up.
@incollection {key440699m,
AUTHOR = {Yor, Marc},
TITLE = {Sur les int\'egrales stochastiques optionnelles
et une suite remarquable de formules
exponentielles [On optional stochastic
integrals and a remarkable series of
exponential formulas]},
BOOKTITLE = {S\'eminaire de probabilit\'es {X} [Tenth
probability seminar]},
EDITOR = {Meyer, P. A.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {511},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1976},
PAGES = {481--500},
DOI = {10.1007/BFb0101123},
URL = {http://www.numdam.org/item?id=SPS_1976__10__481_0},
NOTE = {MR:440699. Zbl:0393.60057.},
ISSN = {0075-8434},
ISBN = {9783540076810},
}
M. Yor :
“Sur quelques approximations d’intégrales stochastiques On some approximations of stochastic integrals ],
pp. 257–297
in
Séminaire de probabilités XI
[Eleventh probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 581 .
Springer (Berlin ),
1977 .
MR
448556 Zbl
0367.60058 incollection
Abstract
People
BibTeX
The investigation concerns the limit of several families of Riemann sums, converging to the Itô stochastic integral of a continuous process with respect to a continuous semimartingale, to the Stratonovich stochastic integral, or to the Stieltjes integral with respect to the bracket of two continuous semimartingales. The last section concerns the stochastic integral of a differential form.
@incollection {key448556m,
AUTHOR = {Yor, Marc},
TITLE = {Sur quelques approximations d'int\'egrales
stochastiques [On some approximations
of stochastic integrals]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XI} [Eleventh
probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {581},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1977},
PAGES = {257--297},
DOI = {10.1007/BFb0087222},
URL = {http://www.numdam.org/item?id=SPS_1977__11__518_0},
NOTE = {MR:448556. Zbl:0367.60058.},
ISSN = {0075-8434},
ISBN = {9783540081456},
}
M. Yor :
“À propos d’un lemme de Ch. Yoeurp On a lemma of Ch. Yoeurp ],
pp. 493–501
in
Séminaire de probabilités XI
[Eleventh probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 581 .
Springer (Berlin ),
1977 .
MR
451396 Zbl
0373.60047 incollection
Abstract
People
BibTeX
Yoeurp’s lemma is the following: if \( A \) is a previsible process of bounded variation, its square bracket \( [A,L] \) with any local martingale \( L \) is a local martingale. This useful result was not easily accessible, thus a complete proof is given, with several new applications — in particular, this characterizes previsible processes of bounded variation among semimartingales.
@incollection {key451396m,
AUTHOR = {Yor, Marc},
TITLE = {\`{A} propos d'un lemme de {C}h.~{Y}oeurp
[On a lemma of {C}h. {Y}oeurp]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XI} [Eleventh
probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {581},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1977},
PAGES = {493--501},
DOI = {10.1007/BFb0087220},
URL = {http://www.numdam.org/item?id=SPS_1977__11__493_0},
NOTE = {MR:451396. Zbl:0373.60047.},
ISSN = {0075-8434},
ISBN = {9783540081456},
}
M. Yor :
“Remarques sur la représentation des martingales comme intégrales stochastiques Remarks on the the representation of martingales as stochastic integrals ],
pp. 502–517
in
Séminaire de probabilités XI
[Eleventh probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 581 .
Springer (Berlin ),
1977 .
MR
458580 Zbl
0367.60046 incollection
Abstract
People
BibTeX
The main result on the relation between the previsible representation property of a set of local martingales and the extremality of their joint law appeared in a celebrated paper of Jacod and Yor Z. für W-theorie , 38 , 1977. Several concrete applications are given here, in particular a complete proof of a “folklore” result on the representation of local martingales of a Lévy process, and a discussion of the commutation problem of [Dellacherie and Stricker 1977].
@incollection {key458580m,
AUTHOR = {Yor, Marc},
TITLE = {Remarques sur la repr\'esentation des
martingales comme int\'egrales stochastiques
[Remarks on the the representation of
martingales as stochastic integrals]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XI} [Eleventh
probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {581},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1977},
PAGES = {502--517},
DOI = {10.1007/BFb0087221},
URL = {https://eudml.org/doc/113134},
NOTE = {MR:458580. Zbl:0367.60046.},
ISSN = {0075-8434},
ISBN = {9783540081456},
}
M. Yor :
“Sur les théories du filtrage et de la prédiction On the theories of filtration and prediction ],
pp. 257–297
in
Séminaire de probabilités XI
[Eleventh probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 581 .
Springer (Berlin ),
1977 .
MR
471060 Zbl
0367.60041 incollection
People
BibTeX
@incollection {key471060m,
AUTHOR = {Yor, Marc},
TITLE = {Sur les th\'eories du filtrage et de
la pr\'ediction [On the theories of
filtration and prediction]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XI} [Eleventh
probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {581},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1977},
PAGES = {257--297},
DOI = {10.1007/BFb0087195},
URL = {http://www.numdam.org/item?id=SPS_1977__11__257_0},
NOTE = {MR:471060. Zbl:0367.60041.},
ISSN = {0075-8434},
ISBN = {9783540081456},
}
M. Yor :
“Grossissement d’une filtration et semi-martingales: Théorèmes généraux Enlargement of a filtration and semi-martingales: General theorems ],
pp. 61–69
in
Séminaire de probabilités XII
[Twelfth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 649 .
Springer (Berlin ),
1978 .
MR
519996 Zbl
0411.60044 incollection
Abstract
People
BibTeX
Given a filtration \( (\mathcal{F}_t) \) and a positive random variable \( L \) , the so-called progressively enlarged filtration is the smallest one \( (\mathcal{G}_t) \) containing \( (\mathcal{F}_t) \) , and for which \( L \) is a stopping time. The enlargement problem consists in describing the semimartingales \( X \) of \( \mathcal{F} \) which remain semimartingales in \( \mathcal{G} \) , and in computing their semimartingale characteristics. In this paper, it is proved that \( X_t\,I_{\{t\lt L\}} \) is a semimartingale in full generality, and that \( X_t\,I_{\{t\geq L\}} \) is a semimartingale whenever \( L \) is honest for \( \mathcal{F} \) , i.e., is the end of an \( \mathcal{F} \) -optional set.
@incollection {key519996m,
AUTHOR = {Yor, Marc},
TITLE = {Grossissement d'une filtration et semi-martingales:
{T}h\'eor\`emes g\'en\'eraux [Enlargement
of a filtration and semi-martingales:
{G}eneral theorems]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XII}
[Twelfth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {649},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
PAGES = {61--69},
DOI = {10.1007/BFb0064595},
URL = {http://www.numdam.org/item?id=SPS_1978__12__61_0},
NOTE = {MR:519996. Zbl:0411.60044.},
ISSN = {0075-8434},
ISBN = {9783540087618},
}
T. Jeulin and M. Yor :
“Grossissement d’une filtration et semi-martingales: Formules explicites Enlargement of a filtration and semi-martingales: Explicit formulas ],
pp. 78–97
in
Séminaire de probabilités XII
[Twelfth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 649 .
Springer (Berlin ),
1978 .
MR
519998 Zbl
0411.60045 incollection
Abstract
People
BibTeX
@incollection {key519998m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Grossissement d'une filtration et semi-martingales:
{F}ormules explicites [Enlargement of
a filtration and semi-martingales: {E}xplicit
formulas]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XII}
[Twelfth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {649},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
PAGES = {78--97},
DOI = {10.1007/BFb0064597},
URL = {http://www.numdam.org/item?id=SPS_1978__12__78_0},
NOTE = {MR:519998. Zbl:0411.60045.},
ISSN = {0075-8434},
ISBN = {9783540087618},
}
C. Dellacherie, P.-A. Meyer, and M. Yor :
“Sur certaines propriétés des espaces de Banach \( H^1 \) et BMO On certain properties of \( H^1 \) Banach and BMO spaces ],
pp. 98–113
in
Séminaire de probabilités XII
[Twelfth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 649 .
Springer (Berlin ),
1978 .
MR
519999 Zbl
0392.60009 incollection
Abstract
People
BibTeX
The general subject is the weak topology \( \sigma(H^1,BMO) \) on the space \( H^1 \) . Its relatively compact sets are characterized by a uniform integrability property of the maximal functions. A sequential completeness a result (a Vitali–Hahn–Saks like theorem) is proved. Finally, a separate section is devoted to the denseness of \( L^{\infty} \) in \( BMO \) , a subject which has greatly progressed since (the Garnett–Jones theorem, see [Émery 1981]; see also [Schachermayer 1996] and [Grandits 1999]).
@incollection {key519999m,
AUTHOR = {Dellacherie, C. and Meyer, P.-A. and
Yor, M.},
TITLE = {Sur certaines propri\'et\'es des espaces
de {B}anach \$H^1\$ et {BMO} [On certain
properties of \$H^1\$ {B}anach and {BMO}
spaces]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XII}
[Twelfth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {649},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
PAGES = {98--113},
DOI = {10.1007/BFb0064598},
URL = {http://www.numdam.org/item?id=SPS_1978__12__98_0},
NOTE = {MR:519999. Zbl:0392.60009.},
ISSN = {0075-8434},
ISBN = {9783540087618},
}
M. Yor :
“Sous-espaces denses dans \( L^1 \) ou \( H^1 \) et représentation des martingales Dense subspaces in \( L^1 \) or \( H^1 \) and representation of martingales ],
pp. 265–309
in
Séminaire de probabilités XII
[Twelfth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 649 .
Springer (Berlin ),
1978 .
With an appendix by the author and J. de Sam Lazaro.
MR
520008 Zbl
0391.60046 incollection
Abstract
People
BibTeX
This paper was a considerable step in the study of the general martingale problem, i.e., of the set \( \mathcal{P} \) of all laws on a filtered measurable space under which a given set \( \mathcal{N} \) of (adapted, right continuous) processes are local martingales. The starting point is a theorem from measure theory due to R. G. Douglas (Michigan Math. J. 11, 1964), and the main technical difference with preceding papers is the systematic use of stochastic integration in \( H^1 \) . The main result can be stated as follows: given a law \( \mathbb{P}\in\mathcal{P} \) , the set \( \mathcal{N} \) has the previsible representation property, i.e., \( \mathcal{F}_0 \) is trivial and stochastic integrals with respect to elements of \( \mathcal{N} \) are dense in \( H^1 \) , if and only if \( \mathbb{P} \) is an extreme point of \( \mathcal{P} \) . Many examples and applications are given.
@incollection {key520008m,
AUTHOR = {Yor, Marc},
TITLE = {Sous-espaces denses dans \$L^1\$ ou \$H^1\$
et repr\'esentation des martingales
[Dense subspaces in \$L^1\$ or \$H^1\$ and
representation of martingales]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XII}
[Twelfth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {649},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
PAGES = {265--309},
DOI = {10.1007/BFb0064607},
URL = {http://www.numdam.org/item?id=SPS_1978__12__265_0},
NOTE = {With an appendix by the author and J.
de Sam Lazaro. MR:520008. Zbl:0391.60046.},
ISSN = {0075-8434},
ISBN = {9783540087618},
}
M. Yor and P.-A. Meyer :
“Sur l’extension d’un théorème de Doob à un noyau \( \sigma \) -fini, d’après G. Mokobodzki On the extension of a theorem of Doob to a \( \sigma \) -finite kernel, after G. Mokobodzki ],
pp. 482–488
in
Séminaire de probabilités XII
[Twelfth probability seminar ].
Edited by C. Dellacherie, P. A. Meyer, and M. Weil .
Lecture Notes in Mathematics 649 .
Springer (Berlin ),
1978 .
MR
520022 Zbl
0391.60047 incollection
Abstract
People
BibTeX
Given a kernel \( K(x,dy) \) consisting of probability measures, all of them absolutely continuous with respect to a measure \( \mu \) , Doob proved long ago using martingale theory that
\[ K(x,dy)=k(x,y)\,\mu(dy) \]
with a jointly measurable density \( k(x,y) \) . What happens if the measures \( K(x,dy) \) are \( \sigma \) -finite? The answer is that Doob’s result remains valid if \( K \) , considered as a mapping
\[ x\mapsto K(x,\,\cdot\,) \]
taking values in the set of all \( \sigma \) -finite measures absolutely continuous w.r.t. \( \mu \) (i.e., of classes of a.s. finite measurable functions), is Borel with respect to the topology of convergence in probability.
@incollection {key520022m,
AUTHOR = {Yor, Marc and Meyer, P.-A.},
TITLE = {Sur l'extension d'un th\'eor\`eme de
{D}oob \`a un noyau \$\sigma\$-fini, d'apr\`es
{G}. {M}okobodzki [On the extension
of a theorem of {D}oob to a \$\sigma\$-finite
kernel, after {G}. {M}okobodzki]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XII}
[Twelfth probability seminar]},
EDITOR = {Dellacherie, C. and Meyer, P. A. and
Weil, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {649},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1978},
PAGES = {482--488},
DOI = {10.1007/BFb0064621},
URL = {http://www.numdam.org/item?id=SPS_1978__12__482_0},
NOTE = {MR:520022. Zbl:0391.60047.},
ISSN = {0075-8434},
ISBN = {9783540087618},
}
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},
}
T. Jeulin and M. Yor :
“Inégalité de Hardy, semimartingales, et faux-amis Hardy’s inequality, semimartingales and false friends ],
pp. 332–359
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
544805 Zbl
0419.60049 incollection
Abstract
People
BibTeX
The main purpose of this paper is to warn against “obvious” statements which are in fact false. Let \( (\mathcal{G}_t) \) be an enlargement of \( (\mathcal{F}_t) \) . Assume that \( \mathcal{F} \) has the previsible representation property with respect to a martingale \( X \) which is a \( \mathcal{G} \) -semimartingale. Then it does not follow that every \( \mathcal{F} \) -martingale \( Y \) is a \( \mathcal{G} \) -semimartingale. Also, even if \( Y \) is a \( \mathcal{G} \) -semimartingale, its \( \mathcal{G} \) -compensator may have bad absolute continuity properties. The counterexample to the first statement involves a detailed study of the initial enlargement of the filtration of Brownian motion \( (B_t)_{t\leq 1} \) by the random variable \( B_1 \) , which transforms it into the Brownian bridge, a semimartingale. Then the stochastic integrals with respect to \( B \) which are \( \mathcal{G} \) -semimartingales are completely described, and this is the place where the classical Hardy inequality appears.
@incollection {key544805m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {In\'egalit\'e de {H}ardy, semimartingales,
et faux-amis [Hardy's inequality, semimartingales
and false friends]},
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 = {332--359},
DOI = {10.1007/BFb0070874},
URL = {http://www.numdam.org/item?id=SPS_1979__13__332_0},
NOTE = {MR:544805. Zbl:0419.60049.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
T. Jeulin and M. Yor :
“Sur l’expression de la dualité entre \( H^1 \) et \( BMO \) On the expression of the duality between \( H^1 \) and \( BMO \) ],
pp. 360–370
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
544806 Zbl
0426.60046 incollection
Abstract
People
BibTeX
@incollection {key544806m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Sur l'expression de la dualit\'e entre
\$H^1\$ et \$BMO\$ [On the expression of
the duality between \$H^1\$ and \$BMO\$]},
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 = {360--370},
DOI = {10.1007/BFb0070875},
URL = {http://www.numdam.org/item?id=SPS_1979__13__360_0},
NOTE = {MR:544806. Zbl:0426.60046.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“Quelques épilogues Some conclusions ],
pp. 400–406
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
544810 Zbl
0427.60040 incollection
Abstract
People
BibTeX
This is an account of current folklore, i.e., small remarks which settle natural questions, possibly published elsewhere but difficult to locate. Among the quotable results, one may mention that if a sequence of martingales converges in \( L^1 \) , one can stop them at arbitrary large stopping times so that the stopped processes converge in \( H^1 \) .
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TITLE = {Quelques \'epilogues [Some conclusions]},
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[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 = {400--406},
DOI = {10.1007/BFb0070879},
URL = {http://www.numdam.org/item?id=SPS_1979__13__400_0},
NOTE = {MR:544810. Zbl:0427.60040.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“In search of a natural definition of optional stochastic integrals 407–426
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
544811 Zbl
0439.60041 incollection
Abstract
People
BibTeX
While the stochastic integral of a previsible process is a very natural object, the optional (compensated) stochastic integral is somewhat puzzling: it concerns martingales only, and depends on the probability law. This paper sketches a “pedagogical” approach, using a version of Fefferman’s inequality for thin processes to characterize those thin processes which are jump processes of local martingales. The results of [Chou 1977], [Lépingle 1977] are easily recovered. Then an attempt is made to extend the optional integral to semimartingales.
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TITLE = {In search of a natural definition of
optional stochastic integrals},
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 = {407--426},
DOI = {10.1007/BFb0070880},
URL = {http://www.numdam.org/item?id=SPS_1979__13__407_0},
NOTE = {MR:544811. Zbl:0439.60041.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“Les filtrations de certaines martingales du mouvement brownien dans \( \mathbb{R}^n \) The filtrations of certain martingales of Brownian motion on \( \mathbb{R}^n \) ],
pp. 427–440
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
544812 Zbl
0418.60057 incollection
Abstract
People
BibTeX
The problem is to study the filtration generated by real valued stochastic integrals
\[ Y=\int_0^t(AX_s, dX_s) ,\]
where \( X \) is a \( n \) -dimensional Brownian motion, \( A \) is a \( n{\times}n \) -matrix, and \( (\,\cdot,\cdot\,) \) is the scalar product. If \( A \) is the identity matrix we thus get (squares of) Bessel processes. If \( A \) is symmetric, we can reduce it to diagonal form, and the filtration is generated by a Brownian motion, the dimension of which is the number of different non-zero eigenvalues of \( A \) . In particular, this dimension is 1 if and only if the matrix is equivalent to \( cI_r \) , a diagonal with \( r \) ones and \( n{-}r \) zeros. This is also (even if the symmetry assumption is omitted) the only case where \( Y \) has the previsible representation property.
@incollection {key544812m,
AUTHOR = {Yor, Marc},
TITLE = {Les filtrations de certaines martingales
du mouvement brownien dans \$\mathbb{R}^n\$
[The filtrations of certain martingales
of {B}rownian motion on \$\mathbb{R}^n\$]},
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 = {427--440},
DOI = {10.1007/BFb0070881},
URL = {http://www.numdam.org/item?id=SPS_1979__13__427_0},
NOTE = {MR:544812. Zbl:0418.60057.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“Sur le balayage des semi-martingales continues On the balayage of continuous semi-martingales ],
pp. 453–471
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
544815 Zbl
0409.60042 incollection
Abstract
People
BibTeX
This paper is independent from the preceding one [El Karoui 1979], and some overlap occurs. The balayage formula is extended to processes \( Z \) which are not locally bounded, and the local time of the semimartingale \( Y \) is computed. The class of continuous semimartingales \( X \) with canonical decomposition \( X=M+V \) such that \( dV \) is carried by
\[ H=\{X=0\} \]
is introduced and studied. It turns out to be an important class, closely related to “relative martingales” [Azéma et al. 1992]. A number of results are given, too technical to be stated here. Stopping previsible, optional and progressive processes at the last exit time \( L \) from \( H \) leads to three \( \sigma \) -fields, \( \mathcal{F}_L^p \) , \( \mathcal{F}_L^o \) , \( \mathcal{F}_L^{\pi} \) , and it was considered surprising that the last two could be different (see [Dellacherie 1978]). Here it is shown that if \( X \) is a continuous uniformly integrable martingale with \( X_0=0 \) ,
\[ \mathbb{E}[X_{\infty}|\mathcal{F}_L^o]=0\neq \mathbb{E}[X_{\infty}|\mathcal{F}_L^{\pi}] .\]
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AUTHOR = {Yor, Marc},
TITLE = {Sur le balayage des semi-martingales
continues [On the balayage of continuous
semi-martingales]},
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 = {453--471},
DOI = {10.1007/BFb0070884},
URL = {http://www.numdam.org/item?id=SPS_1979__13__453_0},
NOTE = {MR:544815. Zbl:0409.60042.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
P.-A. Meyer, C. Stricker, and M. Yor :
“Sur une formule de la théorie du balayage On a formula from balayage theory ],
pp. 478–487
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
544817 Zbl
0415.60031 incollection
Abstract
People
BibTeX
It is shown here that under the same hypotheses, the semimartingale \( Z_{g_t}X_t \) is a sum of three terms: the stochastic integral \( \int_0^t \zeta_s dX_s \) , where \( \zeta \) is the previsible projection of \( Z \) , an explicit sum of jumps involving \( Z-\zeta \) , and a mysterious continuous process with finite variation \( (R_t) \) such that \( dR_t \) is carried by \( H \) , equal to 0 if \( Z \) was optional.
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TITLE = {Sur une formule de la th\'eorie du balayage
[On a formula from balayage theory]},
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 = {478--487},
DOI = {10.1007/BFb0070886},
URL = {http://www.numdam.org/item?id=SPS_1979__13__478_0},
NOTE = {MR:544817. Zbl:0415.60031.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“Sur le supremum du mouvement brownien: Les théorèmes de P. Lévy et J. Pitman On the supremum of Brownian motion: The theorems of P. Lévy and J. Pitman ],
pp. 528–532
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 an appendix of T. Jeunlin’s article “Un théorème de J.W. Pitman”.
MR
544821 Zbl
0422.60028 incollection
People
BibTeX
@incollection {key544821m,
AUTHOR = {Yor, Marc},
TITLE = {Sur le supremum du mouvement brownien:
{L}es th\'eor\`emes de {P}. {L}\'evy
et {J}. {P}itman [On the supremum of
{B}rownian motion: {T}he theorems of
{P}. {L}\'evy and {J}. {P}itman]},
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 = {528--532},
DOI = {10.1007/BFb0070890},
URL = {http://www.numdam.org/item?id=SPS_1979__13__521_0},
NOTE = {This is an appendix of T. Jeunlin's
article ``Un th\'eor\`eme de J.W. Pitman''.
MR:544821. Zbl:0422.60028.},
ISSN = {0075-8434},
ISBN = {9783540095057},
}
M. Yor :
“Un exemple de J. Pitman An example of J. Pitman ],
pp. 624
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
544831 Zbl
0422.60029 incollection
Abstract
People
BibTeX
The balayage formula allows the construction of many martingales vanishing on the zeros of a given continuous martingale \( X \) , namely martingales of the form \( Z_{g_t}X_t \) where \( Z \) is previsible. Taking \( X \) to be Brownian motion, an example is given of a martingale vanishing on its zeros which is not of the above form.
@incollection {key544831m,
AUTHOR = {Yor, M.},
TITLE = {Un exemple de {J}. {P}itman [An example
of {J}. {P}itman]},
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 = {624},
DOI = {10.1007/BFb0070900},
URL = {http://www.numdam.org/item?id=SPS_1979__13__624_0},
NOTE = {MR:544831. Zbl:0422.60029.},
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},
}
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 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
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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},
}
J. W. Pitman and M. Yor :
“Quelques identités en loi pour les processus de Bessel ”
[Some identities in law for Bessel processes ],
pp. 249–276
in
Hommage à P. A. Meyer et J. Neveu
[In homage to P. A. Meyer and J. Neveu ].
Astérisque 236 .
Société Mathématique de France (Paris ),
1996 .
MR
1417987 Zbl
0863.60035 incollection
People
BibTeX
@incollection {key1417987m,
AUTHOR = {Pitman, J. W. and Yor, M.},
TITLE = {Quelques identit\'es en loi pour les
processus de {B}essel [Some identities
in law for {B}essel processes]},
BOOKTITLE = {Hommage \`a {P}.~{A}. {M}eyer et {J}.
{N}eveu [In homage to {P}.~{A}. {M}eyer
and {J}. {N}eveu]},
SERIES = {Ast\'erisque},
NUMBER = {236},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
ADDRESS = {Paris},
YEAR = {1996},
PAGES = {249--276},
NOTE = {MR:1417987. Zbl:0863.60035.},
ISSN = {0303-1179},
}
M. Yor :
“Deux maîtres ès probabilités: Laurent Schwartz et Paul-André Meyer ”
[Two masters of probability: Laurent Schwartz and Paul-André Meyer ],
Gaz. Math., Soc. Math. Fr.
98
(2003 ),
pp. 119–122 .
An English translation appeared as part of a multi-author tribute to Schwartz in Notices Am. Math. Soc. 50 :9 (2003) .
MR
2067357 article
People
BibTeX
@article {key2067357m,
AUTHOR = {Yor, Marc},
TITLE = {Deux ma\^itres \`es probabilit\'es:
{L}aurent {S}chwartz et {P}aul-{A}ndr\'e
{M}eyer [Two masters of probability:
{L}aurent {S}chwartz and {P}aul-{A}ndr\'e
{M}eyer]},
JOURNAL = {Gaz. Math., Soc. Math. Fr.},
FJOURNAL = {Gazette des Math\'ematiciens},
VOLUME = {98},
YEAR = {2003},
PAGES = {119--122},
NOTE = {An English translation appeared as part
of a multi-author tribute to Schwartz
in \textit{Notices Am. Math. Soc.} \textbf{50}:9
(2003). MR:2067357.},
ISSN = {0224-8999},
}
In memoriam Paul-André Meyer: Séminaire de probabilités XXXIX In memoriam Paul-André Meyer: Thirty-ninth probability seminar ].
Edited by M. Émery and M. Yor .
Lecture Notes in Mathematics 1874 .
Springer (Berlin ),
2006 .
MR
2265371 Zbl
1092.60003 book
People
BibTeX
@book {key2265371m,
TITLE = {In memoriam {P}aul-{A}ndr\'e {M}eyer:
{S}\'eminaire de probabilit\'es {XXXIX}
[In memoriam {P}aul-{A}ndr\'e {M}eyer:
{T}hirty-ninth probability seminar]},
EDITOR = {\'Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1874},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {viii+417},
DOI = {10.1007/b128398},
NOTE = {MR:2265371. Zbl:1092.60003.},
ISSN = {0075-8434},
ISBN = {9783540309949},
}
M. Yor :
“The life and scientific work of Paul-André Meyer (August 21st, 1934–January 30th, 2003): ‘Un modèle pour nous tous’ The life and scientific work of Paul-André Meyer (August 21st, 1934–January 30th, 2003): ‘A model for us all’ ],
pp. 13–26
in
In memoriam Paul-André Meyer: Séminaire de probabilités, XXXIX
[In memoriam Paul-André Meyer: Thirty-ninth probability seminar ].
Edited by M. Émery and M. Yor .
Lecture Notes in Mathematics 1874 .
Springer (Berlin ),
2006 .
MR
2276885 Zbl
1216.01025 incollection
Abstract
People
BibTeX
The life and scientific works of Paul André Meyer are presented, with some special emphasis on the contents of the Séminaires de Probabilités and the treatise Probabilités et Potentiel, both of which were key achievements in the career of Paul André Meyer.
@incollection {key2276885m,
AUTHOR = {Yor, Marc},
TITLE = {The life and scientific work of {P}aul-{A}ndr\'e
{M}eyer ({A}ugust 21st, 1934--{J}anuary
30th, 2003): ``{U}n mod\`ele pour nous
tous'' [The life and scientific work
of {P}aul-{A}ndr\'e {M}eyer ({A}ugust
21st, 1934--{J}anuary 30th, 2003): ``{A}
model for us all'']},
BOOKTITLE = {In memoriam {P}aul-{A}ndr\'e {M}eyer:
{S}\'eminaire de probabilit\'es, {XXXIX}
[In memoriam {P}aul-{A}ndr\'e {M}eyer:
{T}hirty-ninth probability seminar]},
EDITOR = {\'Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1874},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {13--26},
DOI = {10.1007/978-3-540-35513-7_2},
NOTE = {MR:2276885. Zbl:1216.01025.},
ISSN = {0075-8434},
ISBN = {9783540309949},
}
D. B. Madan and M. Yor :
“Itô’s integrated formula for strict local martingales 157–170
in
In memoriam Paul-André Meyer: Séminaire de probabilités, XXXIX
[In memoriam Paul-André Meyer: Thirty-ninth probability seminar ].
Edited by M. Émery and M. Yor .
Lecture Notes in Mathematics .
Springer (Berlin ),
2006 .
MR
2276895 Zbl
1133.60025 incollection
Abstract
People
BibTeX
For \( F:\mathbb{R}\to\mathbb{R} \) a \( C^2 \) function, and more generally a difference of convex functions, \( (S_t \) , \( t\geq 0) \) a continuous strict local martingale taking values in \( \mathbb{R}_+ \) , we investigate under which condition the stochastic integral appearing in Itô’s formula applied to \( F(S_t) \) , \( t\geq 0 \) , is a true martingale and, if not, how it may be corrected to become one.
@incollection {key2276895m,
AUTHOR = {Madan, Dilip B. and Yor, Marc},
TITLE = {It\^o's integrated formula for strict
local martingales},
BOOKTITLE = {In memoriam {P}aul-{A}ndr\'e {M}eyer:
{S}\'eminaire de probabilit\'es, {XXXIX}
[In memoriam {P}aul-{A}ndr\'e {M}eyer:
{T}hirty-ninth probability seminar]},
EDITOR = {\'Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {157--170},
DOI = {10.1007/978-3-540-35513-7_13},
NOTE = {MR:2276895. Zbl:1133.60025.},
ISSN = {1874},
ISBN = {9783540309949},
}
B. Roynette, P. Vallois, and M. Yor :
“Pénalisations et quelques extensions du théorème de Pitman, relatives au mouvement Brownien et à son maximum unilatère Penalizations and some extensions of Pitman’s theorem relative to Brownian motion and its one-sided maximum ],
pp. 305–336
in
In memoriam Paul-André Meyer: Séminaire de probabilités XXXIX
[In memoriam Paul-André Meyer: Thirty-ninth probability seminar ].
Edited by M. Émery and M. Yor .
Lecture Notes in Mathematics 1874 .
Springer (Berlin ),
2006 .
MR
2276902 Zbl
1124.60034 incollection
People
BibTeX
@incollection {key2276902m,
AUTHOR = {Roynette, Bernard and Vallois, Pierre
and Yor, Marc},
TITLE = {P\'enalisations et quelques extensions
du th\'eor\`eme de {P}itman, relatives
au mouvement {B}rownien et \`a son maximum
unilat\`ere [Penalizations and some
extensions of {P}itman's theorem relative
to {B}rownian motion and its one-sided
maximum]},
BOOKTITLE = {In memoriam {P}aul-{A}ndr\'e {M}eyer:
{S}\'eminaire de probabilit\'es {XXXIX}
[In memoriam {P}aul-{A}ndr\'e {M}eyer:
{T}hirty-ninth probability seminar]},
EDITOR = {\'Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1874},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {305--336},
DOI = {10.1007/978-3-540-35513-7_20},
NOTE = {MR:2276902. Zbl:1124.60034.},
ISSN = {0075-8434},
ISBN = {9783540309949},
}
L. Gallardo and M. Yor :
“Some remarkable properties of the Dunkl martingales 337–356
in
In memoriam Paul-André Meyer: Séminaire de probabilités, XXXIX
[In memoriam Paul-André Meyer: Thirty-ninth probability seminar ].
Edited by M. Émery and M. Yor .
Lecture Notes in Mathematics .
Springer (Berlin ),
2006 .
MR
2276903 Zbl
1128.60027 incollection
Abstract
People
BibTeX
In this paper, we study a class, depending on a parameter \( k\geq 0 \) , of real valued Feller processes
\[ X^{(k)} = (X_t^{(k)})_{t\gt 0} ,\]
the so called Dunkl processes which are martingales satisfying the Brownian scaling property. These processes are the only martingales whose absolute value is a Bessel process. Moreover, the absolute continuity and intertwining relations valid for some pairs of Bessel processes may be generalized to Dunkl processes. The main result of the paper is a mixed chaotic representation property for the \( L^2 \) space of the martingale \( X^{(k)} \) in terms of its continuous part (which is a Brownian motion) and its purely discontinuous part, a martingale \( \gamma \) with bracket \( \langle\gamma\rangle_t = 2kt \) .
@incollection {key2276903m,
AUTHOR = {Gallardo, L\'eonard and Yor, Marc},
TITLE = {Some remarkable properties of the {D}unkl
martingales},
BOOKTITLE = {In memoriam {P}aul-{A}ndr\'e {M}eyer:
{S}\'eminaire de probabilit\'es, {XXXIX}
[In memoriam {P}aul-{A}ndr\'e {M}eyer:
{T}hirty-ninth probability seminar]},
EDITOR = {\'Emery, M. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {337--356},
DOI = {10.1007/978-3-540-35513-7_21},
NOTE = {MR:2276903. Zbl:1128.60027.},
ISSN = {1874},
ISBN = {9783540309949},
}
