Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839944 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 15 Pages |
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 1/21/2. 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 1/21/2 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.
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Authors
Mamadou A. Diop, María J. Garrido-Atienza,