Approximate controllability of stochastic equations in a Hilbert space with fractional Brownian motions

Abstract

In this paper, the approximate controllability for semilinear stochastic equations in Hilbert spaces is studied. The additive noise is the formal derivative of a fractional Brownian motion in a Hilbert space with the Hurst parameter in the interval (½, 1). Sufficient conditions are established. The results are obtained by using the Banach fixed point theorem.