Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Strict positivity of the density for a Poisson driven S.D.E.

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider a one-dimensional stochastic differential equation driven by a compensated Poisson measure. We assume that this equation admits a solution $X_t$, and that for some $T>0$, the law of $X_T$ admits a continuous density with respect to the Lebesgue measure on $\reel$. We prove that under a strong non-degeneracy condition, this density is strictly positive on $\reel$. To this aim, we develop Bismut's approach of the Malliavin calculus for Poisson functionals.

Mots Clés: Stochastic differential equations ; Jump processes ; Stochastic calculus of variations

Date: 1999-05-04

Prépublication numéro: PMA-500