Large deviation principle of occupation measures for Non-linear monotone SPDEs

TL;DR

This paper establishes a large deviation principle for occupation measures of certain non-linear monotone SPDEs using hyper-exponential recurrence, with applications to various concrete equations driven by stable noises.

Contribution

It introduces a novel large deviation framework for non-linear monotone SPDEs and applies it to multiple specific equations with stable noise drivers.

Findings

Large deviation principle proven for a class of non-linear monotone SPDEs.

Applicable to equations like stochastic p-Laplace, porous medium, and Ginzburg-Landau.

Results extend understanding of probabilistic behavior of complex SPDEs.

Abstract

Using the hyper-exponential recurrence criterion, a large deviation principle for the occupation measure is derived for a class of non-linear monotone stochastic partial differential equations. The main results are applied to many concrete SPDEs such as stochastic $p$-Laplace equation, stochastic porous medium equation, stochastic fast-diffusion equation, and even stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises.