Energy image density property and the lent particle method for Poisson measures

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 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 the lent particle method for Poisson measures. Journal of Functional Analysis, 2009, ⟨10.1016/j.jfa.2009.03.004⟩. ⟨hal-00296582v3⟩