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 representationNature: Original
Retrieve article from Numdam
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
1312Keywords: Stochastic exponentials,
Semimartingales,
Multiplicative decompositionNature: Original Retrieve article from Numdam
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 characteristicsNature: Original Retrieve article from Numdam
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,
TightnessNature: Original Retrieve article from Numdam
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 $\Omega\times
R$ 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
1228Keywords: Fuzzy random variables,
Convergence in lawNature: Original Retrieve article from Numdam
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 Retrieve article from Numdam
XVII: 36, 371-376, LNM 986 (1983)
MÉMIN, Jean
Sur la contiguïté relative de deux suites de mesures. Compléments Retrieve article from Numdam
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 Retrieve article from Numdam
XXV: 16, 162-177, LNM 1485 (1991)
MÉMIN, Jean;
SŁOMIŃSKI, Leszek
Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques Retrieve article from Numdam
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 Retrieve article from Numdam
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) Retrieve article from Numdam
XXXV: 21, 306-328, LNM 1755 (2001)
COQUET, François;
MÉMIN, Jean;
SŁOMIŃSKI, Leszek
On weak convergence of filtrations Retrieve article from Numdam
XXXIX: 03, 81-116, LNM 1874 (2006)
COQUET, François;
JAKUBOWSKI, Adam;
MÉMIN, Jean;
SŁOMIŃSKI, Leszek
Natural decomposition of processes and weak Dirichlet processes
