Tuesday, September 29, 2009
10:30 AM in HAAS 111
Michael Röckner
Fakultät für Mathematik, Universität Bielefeld, Germany

Fokker--Planck equations on Hilbert spaces

Abstract

We consider a stochastic differential equation in Hilbert space with time dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, existence and uniqueness of a measure valued solution, for the corresponding Fokker-Planck equation. In particular, we verify the Chapman-Kolmogorov equations and get an evolution system of transition probabilities for the stochastic dynamics informally given by the stochastic differential equation.