Energy image density property and local gradient for Poisson random measures

Nicolas Bouleau (1, 2) , Laurent Denis (3)

1 CIRED - centre international de recherche sur l'environnement et le développement
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
3 Département de Mathématiques (Evry)

We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the {\it energy image density} property for Dirichlet forms and on what we call {\it the lent particle method} which consists in adding a particle and taking it back after some calculation.

Mots clés: Poisson functionals; Dirichlet Forms; Energy Image Density; Lévy Processes; Gradient

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Nicolas Bouleau, Laurent Denis. Energy image density property and local gradient for Poisson random measures. 2008. ⟨hal-00296582v2⟩