Drichlet forms for Poisson measures and Lévy processes : the lent particle method

Nicolas Bouleau (1) , Laurent Denis (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 Département de Mathématiques (Evry)

We present a new approach to absolute continuity of laws of Poisson functionals. The theoretical framework is that of local Dirichlet forms as a tool to study probability spaces. The method gives rise to a new explicit calculus that we show first on some simple examples : it consists in adding a particle and taking it back after computing the gradient. Then we apply it to SDE's driven by Poisson measure.

Mots clés: Dirichlet forms; random Poisson measures; Lévy processes; stochastic differential equations

Domaines: Probabilités [math.PR]

Nicolas Bouleau, Laurent Denis. Drichlet forms for Poisson measures and Lévy processes : the lent particle method. Workshop on Stochastic Analysis and Finance Hong-Kong 2009, Jun 2009, Hong-Kong, Hong Kong SAR China. pp.3-20. ⟨hal-00781424⟩