Convergences de Martingales a valeurs Vectorielles
Convex concentration inequalities and forward-backward stochastic calculus.
Convex hulls, Sticky particle dynamics and Pressure-less gas system
We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities with negative jumps. We show the existence of a stochastic process and a forward flow satisfying and , where is the law of and is the velocity of particle at time . Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map is the entropy solution of a scalar conservation law where the flux represents the particles...
Correction : «À propos de l'intégrabilité uniforme des martingales exponentielles»
Correction à un article d'Attal et Émery sur «les martingales d'Azéma bidimensionnelles»
Correction : «Quelques cas de représentation chaotique»
Correction : «Temps local pour les martingales à deux indices par rapport à sa variation quadratique»
Corrections : «Décomposition des martingales locales et raréfaction des sauts»
Curve crossing for the reflected Lev́y process at zero and infinity.
Décomposition atomique de martingales de la classe
Décomposition de Kunita-Watanabe
Décomposition des martingales locales et raréfaction des sauts
Decomposition of two parameter martingales.
In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.
Décompositions multiplicatives de semimartingales exponentielles et applications
Demiconvergence of processes indexed by two indices
Démonstration «atomique» des inégalités de Burkholder-Davis-Gundy
Démonstration d'un théorème de F. Knight à l'aide de martingales exponentielles
Démonstration élémentaire d'un résultat d'Azéma et Jeulin
Démonstration simple d'un résultat sur le temps local
Density estimation via best -approximation on classes of step functions
We establish consistent estimators of jump positions and jump altitudes of a multi-level step function that is the best -approximation of a probability density function . If itself is a step-function the number of jumps may be unknown.