Evolution Equations Driven by a Fractional White Noise in Spaces of Abstract Stochastic Distributions

In this paper we study stochastic evolution equations driven by a fractional white noise with arbitrary Hurst parameter in infinite dimension. We establish the existenceand uniqueness of a mild solution for a nonlinear equation with multiplicative noise under Lipschitz condition by using a fixed point argument in an appropriate inductive limit space. In the linear case with additive noise a strong solution is obtained. Those results are applied to stochastic parabolic partial differentialequations perturbed by a fractional white noise.