A fractional stochastic evolution equation driven by fractional Brownian motion

Abstract

This paper introduces a semilinear stochastic evolution equation which contains fractional powers of the infinitesimal generator of a strongly continuous semigroup and is driven by Hilbert space-valued fractional Brownian motion. Fractional powers of the generator induce long-range dependence in space, while fractional Brownian motion induces long-range dependence in time in the solution of the equation. An approximation of the evolution solution is then constructed by the splitting method. The existence and uniqueness of the solution and mean-square convergence of the approximation algorithm are established.