Approximate solutions for a class of stochastic evolution equations with variable delays. II

Abstract

This is a continuation of our previous paper [9] where we established the Carathéodory approximate solution for a stochastic evolution equation with variable delay in Hilbert space of the form when the coefficients f and g were Lipschitz. In this paper we shall show the same approximate solution for the delay equation but the coefficients f and g are supposed to be weaker than Lipschitz continuity. The proof of the convergence of the Carathéodory approximation represents an alternative to the procedure for establishing the existence and uniqueness of the solution to the delay equation