Strong Solutions of Stochastic Differential Inclusions with Unbounded Right-Hand Side in a Hilbert Space

Abstract

In a separable Hilbert space, a stochastic differential inclusion with coefficients whose values are closed not necessarily convex sets is considered. Two existence theorems for strong solutions are proved. In the first theorem, the proof is based on the use of Euler polygonal lines; in the second, on the successive approximation method. Instead of the assumption that the coefficients of the inclusion are globally Lipschitz, which is traditional in such cases, some conditions that are less restrictive for the problems in question are used.