Stochastic lattice dynamical systems with fractional noise

TL;DR

This paper studies stochastic lattice dynamical systems driven by fractional Brownian motion with Hurst parameter greater than 1/2, establishing existence, uniqueness, and stability of solutions within a random dynamical systems framework.

Contribution

It introduces a novel approach to analyze such systems using Young integration, proving existence, uniqueness, and stability results that extend previous models.

Findings

Existence and uniqueness of solutions established

Solutions generate a random dynamical system

Exponential stability of the trivial solution proven

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.