Browse by: Author name - Classification - Keywords - Nature

13 matches found
X: 03, 24-39, LNM 511 (1976)
JACOD, Jean; MÉMIN, Jean
Un théorème de représentation des martingales pour les ensembles régénératifs (Martingale theory, Markov processes, Stochastic calculus)
The natural filtration of a regenerative set $M$ is that of the corresponding age process''. There is a natural optional random measure $\mu$ carried by the right endppoints of intervals contiguous to $M$, each endpoint carrying a mass equal to the length of its interval. Let $\nu$ be the previsible compensator of $\mu$. It is shown that, if $M$ has an empty interior the martingale measure $\mu-\nu$ has the previsible representation property in the natural filtration
Comment: Martingales in the filtration of a random set (not necessarily regenerative) have been studied by Azéma in 1932. In the case of the set of zeros of Brownian motion, the martingale considered here is the second Azéma's martingale'' (not the well known one which has the chaotic representation property)
Keywords: Regenerative sets, Renewal theory, Stochastic integrals, Previsible representation
Nature: Original
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XII: 04, 35-46, LNM 649 (1978)
MÉMIN, Jean
Décompositions multiplicatives de semimartingales exponentielles et applications (General theory of processes)
It is shown that, given two semimartingales $U,V$ such that $U$ has no jump equal to $-1$, there is a unique semimartingale $X$ such that ${\cal E}(X)\,{\cal E}(U)={\cal E}(V)$. This result is applied to recover all known results on multiplicative decompositions
Comment: The results of this paper are used in Mémin-Shiryaev 1312
Keywords: Stochastic exponentials, Semimartingales, Multiplicative decomposition
Nature: Original
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XIII: 12, 142-161, LNM 721 (1979)
MÉMIN, Jean; SHIRYAEV, Albert N.
Un critère prévisible pour l'uniforme intégrabilité des semimartingales exponentielles (Martingale theory)
A condition is given so that the stochastic exponential of a special semimartingale $X$ is a uniformly integrable process. It involves only the local characteristics of $X$, i.e., its previsible compensator, Lévy measure, and quadratic variation of the continuous martingale part. The proof rests on multiplicative decompositions, and known results in the case of martingales
Keywords: Stochastic exponentials, Semimartingales, Multiplicative decomposition, Local characteristics
Nature: Original
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XIV: 27, 227-248, LNM 784 (1980)
JACOD, Jean; MÉMIN, Jean
Sur la convergence des semimartingales vers un processus à accroissements indépendants (General theory of processes, Stochastic calculus, Martingale theory)
A method of Kabanov, Liptzer and Shiryaev is adapted to study the convergence of a sequence of semimartingales to a process with independent increments (to be completed)
Keywords: Convergence in law, Tightness
Nature: Original
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XV: 36, 529-546, LNM 850 (1981)
JACOD, Jean; MÉMIN, Jean
Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité (Measure theory)
For simplicity we consider only real valued r.v.'s, but it is essential that the paper considers general Polish spaces instead of $R$. Let us define a fuzzy r.v. $X$ on $(\Omega, {\cal F},P)$ as a probability measure on $\Omega\timesR$ whose projection on $\Omega$ is $P$. In particular, a standard r.v. $X$ defines such a measure as the image of $P$ under the map $\omega\mapsto (\omega,X(\omega))$. The space of fuzzy r.v.'s is provided with a weak topology, associated with the bounded functions $f(\omega,x)$ which are continuous in $x$ for every $\omega$, or equivalently with the functions $I_A(\omega)\,f(x)$ with $f$ bounded continuous. The main topic of this paper is the study of this topology
Comment: From this description, it is clear that this paper extends to general Polish spaces the topology of Baxter-Chacon (forgetting about the filtration), for which see 1228
Keywords: Fuzzy random variables, Convergence in law
Nature: Original
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XVI: 28, 319-337, LNM 920 (1982)
EAGLESON, G.K.; MÉMIN, Jean
Sur la contiguïté de deux suites de mesures : généralisation d'un théorème de Kabanov-Liptser-Shiryayev
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XVII: 36, 371-376, LNM 986 (1983)
MÉMIN, Jean
Sur la contiguïté relative de deux suites de mesures. Compléments
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XVII: 44, 509-511, LNM 986 (1983)
JACOD, Jean; MÉMIN, Jean
Rectification à Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité
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XXV: 16, 162-177, LNM 1485 (1991)
MÉMIN, Jean; SŁOMIŃSKI, Leszek
Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques
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XXVIII: 22, 279-292, LNM 1583 (1994)
COQUET, François; MÉMIN, Jean
Vitesse de convergence en loi pour des solutions d'équations différentielles stochastiques vers une diffusion
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XXXI: 32, 327-328, LNM 1655 (1997)
COQUET, François; MÉMIN, Jean
Correction à : Vitesse de convergence en loi pour des solutions d'équations différentielles stochastiques vers une diffusion (volume~XXVIII)
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XXXV: 21, 306-328, LNM 1755 (2001)
COQUET, François; MÉMIN, Jean; SŁOMIŃSKI, Leszek
On weak convergence of filtrations
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XXXIX: 03, 81-116, LNM 1874 (2006)
COQUET, François; JAKUBOWSKI, Adam; MÉMIN, Jean; SŁOMIŃSKI, Leszek
Natural decomposition of processes and weak Dirichlet processes