Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems

TL;DR

This paper investigates the large deviation principles of invariant measures in stochastic reaction-diffusion lattice systems with multiplicative noise, linking stochastic and deterministic systems and establishing comprehensive deviation results.

Contribution

It introduces new large deviation results for invariant measures of stochastic reaction-diffusion lattice systems, combining tail-end estimates and weighted space arguments.

Findings

Invariant measures converge to deterministic invariant measures as noise vanishes.

Established uniform large deviation principles for solution paths over initial data.

Proved large deviations of invariant measures using tail-end estimates and weighted spaces.

Abstract

In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic system must be an invariant measure of the deterministic limiting system as noise intensity approaches zero. We then prove the uniform Freidlin-Wentzell large deviations of solution paths over all initial data and the uniform Dembo-Zeitouni large deviations of solution paths over a compact set of initial data. We finally establish the large deviations of invariant measures by combining the idea of tail-ends estimates and the argument of weighted spaces.