APPROXIMATE SOLUTIONS FOR A CLASS OF STOCHASTIC-EVOLUTION EQUATIONS WITH VARIABLE DELAYS

Abstract

The objective of this paper is to give the Caratheodory approximation solution for a stochastic evolution equation with variable delay in Hilbert spaces of the form dx(t) = f(x(t), x(t - tau(t)), t) dt + g(x(t), x(t - tau(t)), t) dw(t) The proof of the convergence of the Caratheodory approximation represents an alternative to the procedure for establishing the existence and uniqueness of the solution to the delay equation. We also overcome the difficulty due to the variable time lag tau(.)