Large Deviations for a Class of Semilinear Stochastic Partial Differential Equations

TL;DR

This paper establishes a large deviations principle for solutions to a class of semilinear stochastic PDEs with multiplicative noise, using an improved weak convergence approach.

Contribution

It introduces a novel proof technique that enhances previous methods for deriving large deviations in semilinear stochastic PDEs.

Findings

LDP proven for a broad class of semilinear SPDEs

Improved weak convergence proof method

Enhanced understanding of solution behavior under rare events

Abstract

We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our proof is based on the weak convergence approach and significantly improves earlier methods.