Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift

Da Prato G, Flandoli F, Priola E, Röckner M. Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift. The Annals Of Probability. 2013;41(5):3306-3344.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. Such restriction, however, is common in infinite dimensions