Wong-Zakai approximation for the dynamics of stochastic evolution equation driven by rough path with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$

TL;DR

This paper studies the approximation of stochastic evolution equations driven by rough paths with Hurst index between 1/3 and 1/2, focusing on the existence and stability of their random attractors.

Contribution

It establishes the existence of random attractors for such equations and proves the upper semi-continuity of these attractors under approximation.

Findings

Existence of random attractors for the considered stochastic evolution equations.

Upper semi-continuity of the attractors with respect to approximation parameters.

Extension of attractor theory to systems driven by rough paths with Hurst index in (1/3, 1/2].

Abstract

In this paper, we obtain the existence of random attractors for a class of evolution equations driven by a geometric fractional Brownian rough path with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$ and establish the upper semi-continuity of random attractors $\mathcal{A}_{\eta}$ for the approximated systems of the evolution equations.