Evolution equations driven by a fractional Brownian motion

Abstract

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter H > 1/2 and nuclear covariance operator. We establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter H. This result is applied to stochastic parabolic equation perturbed by a fractional white noise. In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if H > d/4. The proofs of our results combine techniques of fractional calculus with semigroup estimates. © 2002 Elsevier Inc. All rights reserved.