Large Deviation Principles of Invariant Measures of Stochastic Reaction-Diffusion Lattice 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.02720
- arXiv:
- arXiv:2405.02720
- Bibcode:
- 2024arXiv240502720W
- Keywords:
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- Mathematics - Probability;
- Mathematics - Dynamical Systems;
- 60F10;
- 60H10;
- 37L55;
- 37L30