II: 01, 1-21, LNM 51 (1968)
AZÉMA, Jacques;
DUFLO, Marie;
REVUZ, Daniel
Classes récurrentes d'un processus de Markov (
Markov processes)
This is an improved version of a paper by the same authors (
Ann. Inst. H. Poincaré, 2, 1966). Its aim is a theory of recurrence in continuous time (for a Hunt process). The main point is to use the finely open sets instead of the ordinary ones to define recurrence
Comment: The subject is further investigated by the same authors in
302Keywords: Recurrent sets,
Fine topologyNature: Original
Retrieve article from Numdam
III: 02, 24-33, LNM 88 (1969)
AZÉMA, Jacques;
DUFLO, Marie;
REVUZ, Daniel
Mesure invariante des processus de Markov récurrents (
Markov processes)
A condition similar to the Harris recurrence condition is studied in continuous time. It is shown that it implies the existence (up to a constant factor) of a unique $\sigma$-finite excessive measure, which is invariant. The invariant measure for a time-changed process is described
Comment: This is related to several papers by the same authors on recurrent Markov processes, and in particular to
201Keywords: Recurrent potential theory,
Invariant measuresNature: Original Retrieve article from Numdam
VI: 02, 35-50, LNM 258 (1972)
AZÉMA, Jacques
Une remarque sur les temps de retour. Trois applications (
Markov processes,
General theory of processes)
This paper is the first step in the investigations of Azéma on the ``dual'' form of the general theory of processes (for which see Azéma (
Ann. Sci. ENS, 6, 1973, and
814). Here the $\sigma$-fields of cooptional and coprevisible sets are introduced in a Markovian set-up, and without their definitive names. A section theorem by return times is proved, and applications to the theory of Markov processes are given
Keywords: Homogeneous processes,
Coprevisible processes,
Cooptional processes,
Section theorems,
Projection theorems,
Time reversalNature: Original Retrieve article from Numdam
VIII: 01, 1-10, LNM 381 (1974)
AZÉMA, Jacques;
MEYER, Paul-André
Une nouvelle représentation du type de Skorohod (
Markov processes)
A Skorohod imbedding theorem for general Markov processes is proved, in which the stopping time is a randomized ``left'' terminal time. A uniqueness result is proved
Comment: The result is deduced from a representation of measures by left additive functionals, due to Azéma (
Invent. Math. 18, 1973 and this volume,
814). A general survey on the Skorohod embedding problem is Ob\lój,
Probab. Surv. 1, 2004
Keywords: Skorohod imbedding,
Multiplicative functionalsNature: Original Retrieve article from Numdam
XIII: 06, 90-115, LNM 721 (1979)
AZÉMA, Jacques;
YOR, Marc
Une solution simple au problème de Skorokhod (
Brownian motion)
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 $E[T]=\sigma^2$. It is shown that if $S_t$ is the one-sided supremum of $X$ at time $t$, $T=\inf\{t:S_t\ge\psi(X_t)\}$ 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
Comment: The subject is further investigated in
1356 and
1441. See also
1515. A general survey on the Skorohod embedding problem is Ob\lój,
Probab. Surv. 1, 2004
Keywords: Skorohod imbeddingNature: Original Retrieve article from Numdam
XIII: 56, 625-633, LNM 721 (1979)
AZÉMA, Jacques;
YOR, Marc
Le problème de Skorokhod~: compléments à l'exposé précédent (
Brownian motion)
What the title calls ``the preceding talk'' is
1306. The method is extended to (centered) measures possessing a moment of order one instead of two, preserving the uniform integrability of the stopped martingale
Comment: A general survey on the Skorohod embedding problem is Ob\lój,
Probab. Surv. 1, 2004
Keywords: Skorohod imbeddingNature: Original Retrieve article from Numdam
XIV: 06, 53-61, LNM 784 (1980)
AZÉMA, Jacques;
GUNDY, Richard F.;
YOR, Marc
Sur l'intégrabilité uniforme des martingales exponentielles (
Martingale theory)
The main result of this paper is the following: Let $X$ be a martingale which is continuous and bounded in $L^1$ (both conditions are essential). Then $X$ is uniformly integrable if and only if $tP\{X^{*}>t\}$ or equivalently $tP\{S(X)>t\}$ tend to $0$ as $t\rightarrow\infty$, where $S(X)$ is the usual square function. The methods (using a good lambda inequality) are close to
1404Comment: Generalized by Takaoka
3313Keywords: Exponential martingales,
Continuous martingalesNature: Original Retrieve article from Numdam
XIX: 32, 397-495, LNM 1123 (1985)
AZÉMA, Jacques
Sur les fermés aléatoires Retrieve article from Numdam
XXI: 17, 262-269, LNM 1247 (1987)
AZÉMA, Jacques;
YOR, Marc
Interprétation d'un calcul de H. Tanaka en théorie générale des processus Retrieve article from Numdam
XXIII: 07, 88-130, LNM 1372 (1989)
AZÉMA, Jacques;
YOR, Marc
Étude d'une martingale remarquable Retrieve article from Numdam
XXIII: 08, 131-138, LNM 1372 (1989)
AZÉMA, Jacques;
HAMZA, Haïs
La propriété de représentation prévisible dans la filtration naturelle d'un ensemble régénératif Retrieve article from Numdam
XXIV: 14, 210-226, LNM 1426 (1990)
AZÉMA, Jacques;
YOR, Marc
Dérivation par rapport au processus de Bessel Retrieve article from Numdam
XXVI: 22, 249-306, LNM 1526 (1992)
AZÉMA, Jacques;
YOR, Marc
Sur les zéros des martingales continues Retrieve article from Numdam
XXVI: 23, 307-321, LNM 1526 (1992)
AZÉMA, Jacques;
MEYER, Paul-André;
YOR, Marc
Martingales relatives Retrieve article from Numdam
XXVII: 15, 133-158, LNM 1557 (1993)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
YOR, Marc
Le théorème d'arrêt en une fin d'ensemble prévisible Retrieve article from Numdam
XXVIII: 20, 236-255, LNM 1583 (1994)
AZÉMA, Jacques;
RAINER, Catherine
Sur l'équation de structure $d{[X,X]}_t=dt-X^+_{t-}dX_t$ Retrieve article from Numdam
XXX: 16, 243-254, LNM 1626 (1996)
AZÉMA, Jacques;
RAINER, Catherine;
YOR, Marc
Une propriété des martingales pures Retrieve article from Numdam
XXX: 20, 312-343, LNM 1626 (1996)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
MOKOBODZKI, Gabriel;
YOR, Marc
Sur les processus croissants de type injectif Retrieve article from Numdam
XXXII: 22, 316-327, LNM 1686 (1998)
AZÉMA, Jacques;
JEULIN, Thierry;
KNIGHT, Frank B.;
YOR, Marc
Quelques calculs de compensateurs impliquant l'injectivité de certains processus croissants Retrieve article from Numdam
XLVII: 01, xi-xxxi, LNM 2137 (2015)
AZÉMA, Jacques;
BARRIEU, Pauline;
BERTOIN, Jean;
CABALLERO, Maria Emilia;
DONATI-MARTIN, Catherine;
ÉMERY, Michel;
HIRSCH, Francis;
HU, Yueyun;
LEDOUX, Michel;
NAJNUDEL, Joseph;
MANSUY, Roger;
MICLO, Laurent;
SHI, Zhan;
WILLIAMS, David
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