Browse by: Author name - Classification - Keywords - Nature

19 matches found
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 302
Keywords: Recurrent sets, Fine topology
Nature: Original
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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 201
Keywords: Recurrent potential theory, Invariant measures
Nature: Original
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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 reversal
Nature: Original
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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 functionals
Nature: Original
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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 imbedding
Nature: Original
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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 imbedding
Nature: Original
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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 1404
Comment: Generalized by Takaoka 3313
Keywords: Exponential martingales, Continuous martingales
Nature: Original
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XIX: 32, 397-495, LNM 1123 (1985)
AZÉMA, Jacques
Sur les fermés aléatoires
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XXI: 17, 262-269, LNM 1247 (1987)
AZÉMA, Jacques; YOR, Marc
Interprétation d'un calcul de H. Tanaka en théorie générale des processus
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XXIII: 07, 88-130, LNM 1372 (1989)
AZÉMA, Jacques; YOR, Marc
Étude d'une martingale remarquable
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XXIII: 08, 131-138, LNM 1372 (1989)
AZÉMA, Jacques; HAMZA, Haïs
La propriété de représentation prévisible dans la filtration naturelle d'un ensemble régénératif
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XXIV: 14, 210-226, LNM 1426 (1990)
AZÉMA, Jacques; YOR, Marc
Dérivation par rapport au processus de Bessel
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XXVI: 22, 249-306, LNM 1526 (1992)
AZÉMA, Jacques; YOR, Marc
Sur les zéros des martingales continues
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XXVI: 23, 307-321, LNM 1526 (1992)
AZÉMA, Jacques; MEYER, Paul-André; YOR, Marc
Martingales relatives
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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
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XXVIII: 20, 236-255, LNM 1583 (1994)
AZÉMA, Jacques; RAINER, Catherine
Sur l'équation de structure $d{[X,X]}_t=dt-X^+_{t-}dX_t$
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XXX: 16, 243-254, LNM 1626 (1996)
AZÉMA, Jacques; RAINER, Catherine; YOR, Marc
Une propriété des martingales pures
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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
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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
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