Random attractors for setvalued dynamical systems for stochastic evolution equations driven by a nontrivial fractional noise

Abstract

We consider a stochastic evolution equation driven by a fractional Brownian motion in a separable Hilbert space with Hurst parameter [Formula: see text]. The coefficient in front of the noise is in general nonlinear. The related integral is a pathwise integral defined by fractional derivatives. The nonlinear coefficients of this equation satisfy weak conditions ensuring only existence of a solution but not uniqueness. This equation generates then a multivalued random dynamical system. We prove the existence of a random attractor for this system.