Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems
Probability
2024-05-07 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2405.02720,
title = {Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice Systems},
author = {Bixiang Wang},
journal= {arXiv preprint arXiv:2405.02720},
year = {2024}
}