Kolmogorov operators and SPDEs

Abstract

The purpose of this paper is to survey a number of selected results on Kolmogorov operators and SPDEs. It consists of two parts: One part is related to Kolmogorov operators and is devoted to the corresponding linear Fokker–Planck–Kolmogorov equations (see [11]), the other part is about three key results about SPDEs obtained resp. published during the last funding period, namely an existence and uniqueness result for $L^2$-initial data for the stochastic total variation flow, a new approach to SPDEs and a pathwise uniqueness result of SDEs on Hilbert spaces with a merely bounded drift part.