Retarded evolution systems driven by fractional Brownian motion with Hurst parameter [formula omitted

Abstract

This paper is devoted to the study of pathwise solutions of delayed evolution systems driven by a Hilbert-valued Hölder-continuous function with Hölder index greater than 1/2. In the first part, we shall obtain the existence and uniqueness of a mild solution for such a system, which turns out to define a non-autonomous dynamical system. In the second part, we consider retarded stochastic systems driven by a Hilbert-valued fractional Brownian motion with Hurst parameter bigger than 1/2 and show that the corresponding mild solutions generate a random dynamical system, provided that the canonical version of the fractional Brownian motion is chosen as the metric dynamical system.