Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations driven by rosenblatt process

Abstract

This paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps. The Banach fixed point theorem and the theory of resolvent operator developed by Grimmer [R.C. Grimmer, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc., 273(1):333-349, 1982] are used. An example illustrates the potential benefits of these results.