Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations

TL;DR

This paper establishes a large deviation principle for a broad class of stochastic evolution equations with small multiplicative noise, enabling analysis of rare events in complex stochastic PDEs.

Contribution

It provides a general framework for large deviations applicable to various quasi-linear stochastic PDEs, including porous medium and reaction-diffusion equations.

Findings

Proves a Freidlin-Wentzell large deviation principle for stochastic evolution equations.

Applicable to stochastic PDEs with polynomial growth and p-Laplacian operators.

Enables analysis of rare events in complex stochastic systems.

Abstract

We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.