M. Yor :
“Représentation des martingales de carré intégrable rélatives aux processus de Wiener et de Poisson à \( n \) paramètres ”
[Representation of square integrable martingales relativeto Wiener and Poisson processes with \( n \) parameters ],
C. R. Acad. Sci., Paris, Sér. A
281 : 2–3
(1975 ),
pp. 111–113 .
A longer article with the same title was published in Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 35 :2 (1976) .
MR
380987
Zbl
0332.60030
article
BibTeX
@article {key380987m,
AUTHOR = {Yor, Marc},
TITLE = {Repr\'esentation des martingales de
carr\'e int\'egrable r\'elatives aux
processus de {W}iener et de {P}oisson
\`a \$n\$ param\`etres [Representation
of square integrable martingales relativeto
{W}iener and {P}oisson processes with
\$n\$ parameters]},
JOURNAL = {C. R. Acad. Sci., Paris, S\'er. A},
FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances
de l'Acad\'emie des Sciences, S\'erie
A},
VOLUME = {281},
NUMBER = {2--3},
YEAR = {1975},
PAGES = {111--113},
NOTE = {A longer article with the same title
was published in \textit{Z. Wahrscheinlichkeitstheorie
und Verw. Gebiete} \textbf{35}:2 (1976).
MR:380987. Zbl:0332.60030.},
ISSN = {0366-6034},
}
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 :
“Une remarque sur les formes de Dirichlet et les semi-martingales ”
[A remark on Dirichlet forms and semi-martingales ],
pp. 283–292
in
Séminaire de théorie du potentiel 2
[Potential theory seminar 2 ]
(Paris, 1975–1976 ).
Edited by F. Hirsch and G. Mokobodzki .
Lecture Notes in Mathematics 563 .
Springer (Berlin ),
1976 .
MR
651572
Zbl
0339.31013
incollection
BibTeX
@incollection {key651572m,
AUTHOR = {Yor, Marc},
TITLE = {Une remarque sur les formes de {D}irichlet
et les semi-martingales [A remark on
{D}irichlet forms and semi-martingales]},
BOOKTITLE = {S\'eminaire de th\'eorie du potentiel
2 [Potential theory seminar 2]},
EDITOR = {Hirsch, F. and Mokobodzki, G.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {563},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1976},
PAGES = {283--292},
DOI = {10.1007/BFb0087584},
NOTE = {(Paris, 1975--1976). MR:651572. Zbl:0339.31013.},
ISSN = {0075-8434},
ISBN = {9783540080572},
}
J. Jacod and M. Yor :
“Étude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales ”
[A study of extremal solution and integral representation of solutions for certain martingale problems ],
Z. Wahrscheinlichkeitstheor. Verw. Geb.
38 : 2
(June 1977 ),
pp. 83–125 .
A brief piece with the same title was earlier published in C. R. Acad. Sci., Paris, Sér. A 283 (1976) .
MR
445604
Zbl
0346.60032
article
BibTeX
@article {key445604m,
AUTHOR = {Jacod, Jean and Yor, Marc},
TITLE = {\'{E}tude des solutions extr\'emales
et repr\'esentation int\'egrale des
solutions pour certains probl\`emes
de martingales [A study of extremal
solution and integral representation
of solutions for certain martingale
problems]},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {38},
NUMBER = {2},
MONTH = {June},
YEAR = {1977},
PAGES = {83--125},
DOI = {10.1007/BF00533303},
NOTE = {A brief piece with the same title was
earlier published in \textit{C. R. Acad.
Sci., Paris, S\'er. A} \textbf{283}
(1976). MR:445604. Zbl:0346.60032.},
ISSN = {0044-3719},
}
C. Yoeurp and M. Yor :
Espace orthogonal à une semi-martingale et applications .
Prépublication ,
Laboratoire de Probabilités, Université Paris VI ,
1977 .
techreport
BibTeX
@techreport {key34179454,
AUTHOR = {C. Yoeurp and M. Yor},
TITLE = {Espace orthogonal \`a une semi-martingale
et applications},
TYPE = {Pr\'epublication},
INSTITUTION = {Laboratoire de Probabilit\'es, Universit\'e
Paris~VI},
YEAR = {1977},
}
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},
}
C. Stricker and M. Yor :
“Calcul stochastique dépendant d’un paramètre ”
[Stochastic calculus dependent on a parameter ],
Z. Wahrscheinlichkeitstheor. Verw. Geb.
45 : 2
(June 1978 ),
pp. 109–133 .
MR
510530
Zbl
0388.60056
article
BibTeX
@article {key510530m,
AUTHOR = {Stricker, C. and Yor, M.},
TITLE = {Calcul stochastique d\'ependant d'un
param\`etre [Stochastic calculus dependent
on a parameter]},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {45},
NUMBER = {2},
MONTH = {June},
YEAR = {1978},
PAGES = {109--133},
DOI = {10.1007/BF00715187},
NOTE = {MR:510530. Zbl:0388.60056.},
ISSN = {0044-3719},
}
P. Brémaud and M. Yor :
“Changes of filtrations and of probability measures ,”
Z. Wahrscheinlichkeitstheor. Verw. Geb.
45 : 4
(December 1978 ),
pp. 269–295 .
MR
511775
Zbl
0415.60048
article
BibTeX
@article {key511775m,
AUTHOR = {Br\'emaud, Pierre and Yor, Marc},
TITLE = {Changes of filtrations and of probability
measures},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {45},
NUMBER = {4},
MONTH = {December},
YEAR = {1978},
PAGES = {269--295},
DOI = {10.1007/BF00537538},
NOTE = {MR:511775. Zbl:0415.60048.},
ISSN = {0044-3719},
}
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},
}
T. Jeulin and M. Yor :
“Nouveaux résultats sur le grossissement des tribus ”
[New results on the enlargement of families ],
Ann. Sci. Éc. Norm. Supér. (4)
11 : 3
(1978 ),
pp. 429–443 .
MR
521639
Zbl
0414.60054
article
People
BibTeX
@article {key521639m,
AUTHOR = {Jeulin, T. and Yor, M.},
TITLE = {Nouveaux r\'esultats sur le grossissement
des tribus [New results on the enlargement
of families]},
JOURNAL = {Ann. Sci. \'Ec. Norm. Sup\'er. (4)},
FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale
Sup\'erieure. Quatri\`eme S\'erie},
VOLUME = {11},
NUMBER = {3},
YEAR = {1978},
PAGES = {429--443},
DOI = {10.24033/asens.1352},
URL = {http://www.numdam.org/item?id=ASENS_1978_4_11_3_429_0},
NOTE = {MR:521639. Zbl:0414.60054.},
ISSN = {0012-9593},
}
M. Yor :
“Sur l’étude des martingales continues extrêmales ”
[On the study of continuous extremal martingales ],
Stochastics
2 : 3
(1979 ),
pp. 191–196 .
MR
528910
Zbl
0409.60043
article
BibTeX
@article {key528910m,
AUTHOR = {Yor, Marc},
TITLE = {Sur l'\'etude des martingales continues
extr\^emales [On the study of continuous
extremal martingales]},
JOURNAL = {Stochastics},
FJOURNAL = {Stochastics},
VOLUME = {2},
NUMBER = {3},
YEAR = {1979},
PAGES = {191--196},
DOI = {10.1080/17442507908833125},
NOTE = {MR:528910. Zbl:0409.60043.},
ISSN = {0090-9491},
}
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},
}
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 \( H^1 \) .
@incollection {key544810m,
AUTHOR = {Yor, Marc},
TITLE = {Quelques \'epilogues [Some conclusions]},
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 = {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 :
“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 \( X_0=0 \) ,
\[ \mathbb{E}[X_{\infty}|\mathcal{F}_L^o]=0\neq \mathbb{E}[X_{\infty}|\mathcal{F}_L^{\pi}] .\]
@incollection {key544815m,
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},
}
M. Yor :
“Loi de l’indice du lacet brownien, et distribution de Hartman–Watson ”
[Law of indices of Brownian laces, and the Hartman–Watson distribution ],
Z. Wahrscheinlichkeitstheor. Verw. Geb.
53 : 1
(January 1980 ),
pp. 71–95 .
MR
576898
Zbl
0436.60057
article
BibTeX
@article {key576898m,
AUTHOR = {Yor, Marc},
TITLE = {Loi de l'indice du lacet brownien, et
distribution de {H}artman--{W}atson
[Law of indices of {B}rownian laces,
and the {H}artman--{W}atson distribution]},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {53},
NUMBER = {1},
MONTH = {January},
YEAR = {1980},
PAGES = {71--95},
DOI = {10.1007/BF00531612},
NOTE = {MR:576898. Zbl:0436.60057.},
ISSN = {0044-3719},
}
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},
}
D. W. Stroock and M. Yor :
“On extremal solutions of martingale problems ,”
Ann. Sci. École Norm. Sup. (4)
13 : 1
(1980 ),
pp. 95–164 .
MR
584083
Zbl
0447.60034
BibTeX
@article {key584083m,
AUTHOR = {Stroock, D. W. and Yor, M.},
TITLE = {On extremal solutions of martingale
problems},
JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale
Sup\'erieure. Quatri\`eme S\'erie},
VOLUME = {13},
NUMBER = {1},
YEAR = {1980},
PAGES = {95--164},
NOTE = {Available at
http://www.numdam.org/item?id=ASENS_1980_4_13_1_95_0.
MR 82b:60051. Zbl 0447.60034.},
ISSN = {0012-9593},
CODEN = {ENAQAF},
}
M. T. Barlow and M. Yor :
“(Semi-) martingale inequalities and local times ,”
Z. Wahrscheinlichkeitstheor. Verw. Geb.
55 : 3
(1981 ),
pp. 237–254 .
MR
608019
Zbl
0451.60050
article
People
BibTeX
@article {key608019m,
AUTHOR = {Barlow, M. T. and Yor, M.},
TITLE = {({S}emi-) martingale inequalities and
local times},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {55},
NUMBER = {3},
YEAR = {1981},
PAGES = {237--254},
DOI = {10.1007/BF00532117},
NOTE = {MR:608019. Zbl:0451.60050.},
ISSN = {0044-3719},
}
M. Yor :
“Inegalités de martingales continues arretées à un temps quelconque ”
[Inequalities of continuous martingales stopping at a random time ],
pp. 110–146
in
Grossissements de filtrations: Exemples et applications
[Enlargements of filtrations: Examples and applications ]
(Paris, 1982–1983 ).
Edited by T. Jeulin and M. Yor .
Lecture Notes in Mathematics 1118 .
Springer (Berlin ),
1985 .
A follow-up paper was also published in Grossissements de filtrations (1985) .
Zbl
0563.60045
incollection
People
BibTeX
@incollection {key0563.60045z,
AUTHOR = {Marc Yor},
TITLE = {Inegalit\'es de martingales continues
arret\'ees \`a un temps quelconque [Inequalities
of continuous martingales stopping at
a random time]},
BOOKTITLE = {Grossissements de filtrations: {E}xemples
et applications [Enlargements of filtrations:
{E}xamples and applications]},
EDITOR = {Jeulin, Th. and Yor, M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1118},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1985},
PAGES = {110--146},
DOI = {10.1007/BFb0075772},
NOTE = {(Paris, 1982--1983). A follow-up paper
was also published in \textit{Grossissements
de filtrations} (1985). Zbl:0563.60045.},
ISSN = {0075-8434},
ISBN = {9783540152101},
}
M. Barlow, J. Pitman, and M. Yor :
“On Walsh’s Brownian motions ,”
pp. 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},
}
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},
}
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},
}
R. Mansuy and M. Yor :
Random times and enlargements of filtrations in a Brownian setting .
Lecture Notes in Mathematics 1873 .
Springer (Berlin ),
2006 .
MR
2200733
Zbl
1103.60003
book
BibTeX
@book {key2200733m,
AUTHOR = {Mansuy, Roger and Yor, Marc},
TITLE = {Random times and enlargements of filtrations
in a {B}rownian setting},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1873},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2006},
PAGES = {xiv+158},
DOI = {10.1007/11415558},
NOTE = {MR:2200733. Zbl:1103.60003.},
ISSN = {0075-8434},
ISBN = {9783540294078},
}
M. Yor :
“On weak and strong Brownian filtrations: Definitions and examples ,”
pp. 115–121
in
Self-similar processes and their applications
(Angers, France, 20–24 July 2009 ).
Edited by L. Chaumont, P. Graczyk, and L. Vostrikova .
Séminaires et Congrès 28 .
Société Mathématique de France (Paris ),
2013 .
MR
3203521
Zbl
1311.60090
incollection
Abstract
BibTeX
This short note consists of 3 parts: [A], [B], [C], which are devoted respectively to: itemize the presentation of the notions of weak and strong Brownian filtrations; the fact that the perturbation of the Brownian filtration under an absolutely continuous change of measure is always weakly Brownian, and sometimes, strictly so; the striking result by B. Tsirel’son that the filtration of the Brownian spider with \( N \) \( (\geq 3) \) legs is strictly weakly Brownian.
@incollection {key3203521m,
AUTHOR = {Yor, Marc},
TITLE = {On weak and strong {B}rownian filtrations:
{D}efinitions and examples},
BOOKTITLE = {Self-similar processes and their applications},
EDITOR = {Chaumont, Lo\"ic and Graczyk, Piotr
and Vostrikova, Lioudmila},
SERIES = {S\'eminaires et Congr\`es},
NUMBER = {28},
PUBLISHER = {Soci\'et\'e Math\'ematique de France},
ADDRESS = {Paris},
YEAR = {2013},
PAGES = {115--121},
URL = {http://smf4.emath.fr/en/Publications/SeminairesCongres/2013/28/html/smf_sem-cong_28_115-121.php},
NOTE = {(Angers, France, 20--24 July 2009).
MR:3203521. Zbl:1311.60090.},
ISSN = {1285-2783},
ISBN = {9782856293652},
}