L2-primitive process for retarded stochastic neutral functional differential equations in Hilbert spaces

Abstract

In this paper, we study the existence of solutions and L2-primitive process for retarded stochastic neutral functional differential equations in Hilbert spaces. We no longer require the Azera-Ascoli theorem to prove the existence of continuous solutions of nonlinear differential systems, but instead we apply the regularity results of general linear differential equations to the case the L2 -primitive process for retarded stochastic neutral functional differential systems with unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term. Finally, we give a simple example to which our main result can be applied