SPD

Abstract

This is a joint work with G. Da Prato, F. Flandoli and M. Rockner. We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on $\R^d$ to infinite dimensions. Because Sobolev regularity results implying continuity or smoothness of functions, do not hold on infinite dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The price we pay is that we can prove uniqueness for a large class, but not for every initial distribution.