The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion

Abstract

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion BH Q (t): dX(t) = (AX(t) + f(t;Xt))dt + g(t)dBH Q (t); with Hurst parameter H 2 (1=2; 1). We also consider the existence of weak solutions.