Existence of Martingale Solutions of Stochastic Differential Inclusions of Parabolic Type in a Hilbert Space

Abstract

We prove that measurable multivalued mappings assuming nonempty closed convex values in Hilbert spaces have progressively measurable selectors. We use this assertion to prove the theorem about the existence of martingale solutions to stochastic differential inclusions of the parabolic type in Hilbert spaces.