Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

Laurent Denis (University of Le Mans, Frankreich)
Thursday, June 25, 2015 - 5:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We present an approach to absolute continuity and regularity of laws of Poisson functionals based on the framework of local Dirichlet forms. The method mainly uses the chaos decomposition of the Poisson L^2 space which extends naturally to a chaos decomposition of the domain of the candidate closed form and gives rise to a new explicit calculus : it consists in adding a particle and taking it back after computing the gradient. This method that we call the lent particle method permits to develop a Malliavin calculus on the Poisson space and to obtain in a simple way existence of density and regularity of laws of Poisson functionals. This talk is devoted to the practice of the method first on some simple examples and then on more sophisticated ones.
This talk is based on several joint works with N. Bouleau and is the subject of a book soon to be released.