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

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 BQH(t): dX(t)=(AX(t)+f(t,Xt))dt+g(t)dBQH(t), with Hurst parameter H∈(1/2,1)H∈(1/2,1). We also consider the existence of weak solutions.