Functional analytic approach to stochastic differential equations II

Michael Roeckner (University of Bielefeld)

Friday 13th June, 2014 11:30-12:30 Maths 516

Abstract

The second lecture will concentrate on the so-called weak approach to SPDE. It relies on a
linearization procedure based on It^o's formula, which transforms the SPDE into a linear PDE for
measures on the state space of the solutions to the SPDE, e.g. on L^2(O), where O is an open,
bounded set in R^d. This linear PDE for measures is just the well-known corresponding Fokker-
Planck-Kolmogorov equation (FPKE), however, on an innite dimensional space (as e.g. L^2(O)),
whose measure valued solutions are just the transition probabilties of the solutions to the underlying SPDE. Recently developed methods to prove existence and uniqueness of solutions to FPKE will be summarized and new results how to construct the solution to the SPDE from the solution of the FPKE will be presented.

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