Potential Analysis

, Volume 38, Issue 1, pp 169–205

Iteration of the Lent Particle Method for Existence of Smooth Densities of Poisson Functionals

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Abstract

In previous works (Bouleau and Denis, J Funct Anal 257:1144–1174, 2009, Probab Theory Relat Fields, 2011) we have introduced a new method called the lent particle method which is an efficient tool to establish existence of densities for Poisson functionals. We now go further and iterate this method in order to prove smoothness of densities. More precisely, we construct Sobolev spaces of any order and prove a Malliavin-type criterion of existence of smooth density. We apply this approach to SDE’s driven by Poisson random measures and also present some non-trivial examples to which our method applies.

Keywords

Stochastic differential equation Poisson functional Dirichlet Form Energy image density Lévy processes Gradient Carré du champ 

Mathematics Subject Classifications (2010)

Primary 60G57 60H05; Secondary 60J45 60G51 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Ecole des PontsParisTech, Paris-EstMarne-La-Vallée Cedex 2France
  2. 2.Equipe Analyse et ProbabilitésUniversité d’Evry-Val-d’EssonneEVRY CedexFrance

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