Existence of Weak Solutions to Stochastic Evolution Inclusions

Abstract

We prove the existence of a weak mild solution to the Cauchy problem for the semilinear stochastic differential inclusion in a Hilbert space where W is a Wiener process, A is a linear operator that generates a C 0-semigroup, F and G are multifunctions with convex compact values satisfying some growth condition, and with respect to the second variable, a condition weaker than the Lipschitz condition. The weak solution is constructed in the sense of Young measures.