Fractional stochastic Volterra equation perturbed by fractional Brownian motion

Abstract

In this paper, we consider a class of fractional stochastic Volterra equation of convolution type driven by infinite dimensional fractional Brownian motion with Hurst index h∈(0,1). Base on the explicit formula for the scalar resolvent function and the properties of the Mittag–Leffler’s function, the existence and regularity results of the stochastic convolution process are established. Separate proofs are required for the cases of Hurst parameter above and below 12 and it will turn out that the regularity of the solution increases with Hurst parameter h.