Stochastic lattice dynamical systems with fractional noise

Abstract

This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such systems by the Young integration setting and prove that the solution generates a random dynamical system. Further, we analyze the exponential stability of the trivial solution.