Tuesday, September 29, 2009
09:30 AM in HAAS 111
Francesco Russo
Institut Galilée,Mathématiques, Université Paris 13, and Projet MATHFI, INRIA Rocquencourt & Cermics Ecole des Ponts

Probabilistic representation of a partial differential equation with monotone discontinuous coefficients and related fields

Abstract

We consider a partial differential equation over the the real line with monotone discontinuous coefficients and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. We will distinguish between two different situations: the so-called non-degenerate and degenerate cases. In the first case we show existence and uniqueness, however in the second one for which we only show existence. Some comments about an associated stochastic PDE with multiplicative noise will be provided. This talk is based on two joint papers: the first with Ph. Blanchard and M. Röckner, the second one with V. Barbu and M. Röckner.