Random Attractors of Stochastic Lattice Dynamical Systems Driven by Fractional Brownian Motions and its Erratum

TL;DR

This paper investigates the existence of unique random attractors for stochastic lattice dynamical systems driven by fractional Brownian motions with Hurst parameter greater than 1/2, and provides an erratum for previous theory misuse.

Contribution

It establishes the existence and uniqueness of a singleton random attractor for these systems under dissipativity conditions, correcting prior theoretical errors.

Findings

Existence of a random dynamical system for SLDS driven by fractional Brownian motions.

Proof of a singleton set as the random attractor.

Correction of previous theoretical misapplication.

Abstract

This paper is devoted to considering the stochastic lattice dynamical systems (SLDS) driven by fractional Brownian motions with Hurst parameter bigger than $1/2$. Under usual dissipativity conditions these SLDS are shown to generate a random dynamical system for which the existence and unique of a random attractor is established. Furthermore, the random attractor is in fact a singleton sets random attractor. Next, we give an erratum because of the misused theory.