Presentation Name: The lent particle method and its applications
Presenter✮: Professor Laurent DENIS
Date: 2014-07-02
Location: 光华东主楼1801
Abstract:

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 work with N. Bouleau.

Annual Speech Directory🤮: No.96

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