Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion

Abstract

This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay functional integro-di erential equations perturbed by a fractional Brownian motion BH, with Hurst parameter H 2 ( 1 2 ; 1). The main tools for the existence of solution is a xed point theorem and the theory of resolvent operators developed in Grimmer [R. Grimmer, Trans. Amer. Math. Soc., 273 (1982), 333{349.], while a Gronwall-type lemma plays the key role for the asymptotic behavior. An example is provided to illustrate the results of this work.