Stochastic representation of partial differential inclusions

Abstract

Partial differential inclusions of the form u t ′ ∈ L F G u + c u and ψ ∈ L FG u + c u , where L FG is a uniformly parabolic second order set-valued operator, are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence and representation theorems for solutions of such type partial differential inclusions are given.