Large deviation principle of occupation measure for stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises

TL;DR

This paper establishes a large deviation principle for occupation measures of a stochastic Ginzburg-Landau equation driven by alpha-stable noises, revealing the exponential ergodicity rate under tau-topology.

Contribution

It introduces a large deviation principle for occupation measures in the context of stochastic Ginzburg-Landau equations with alpha-stable noise, providing new insights into ergodic behavior.

Findings

Large deviation principle established for occupation measures.

Exact exponential ergodicity rate obtained.

Results applicable to stochastic systems with alpha-stable noises.

Abstract

We shall establish a large deviation principle for some occupation measure of the stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises. As a consequence, we obtain the exact rate of exponential ergodicity of the stochastic system under $\tau$-topology.