Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs

Richard F. Bass, Edwin A. Perkins

Published 2011-02-25, updated 2012-05-25Version 2

We prove uniqueness in law for a class of parabolic stochastic partial differential equations in an interval driven by a functional A(u) of the temperature u times a space-time white noise. The functional A(u) is H\"older continuous in u of order greater than 1/2. Our method involves looking at an associated system of infinite-dimensional stochastic differential equations and we obtain a uniqueness result for such systems.