Large deviations for stationary measures of stochastic nonlinear wave equation with smooth white noise

TL;DR

This paper establishes a large deviations principle for stationary measures of stochastic nonlinear wave equations driven by smooth white noise, without requiring unique equilibria or noise roughness, marking a first in PDEs.

Contribution

It proves the Freidlin-Wentzell large deviations principle for stationary measures of stochastic NLW equations without assumptions of unique equilibrium or noise roughness, advancing PDE large deviations theory.

Findings

First large deviations result for PDE stationary measures

No need for unique equilibrium assumption

Applicable to smooth white noise

Abstract

We prove the Freidlin-Wentzell type large deviations principle for the family of stationary measures of stochastic nonlinear wave (NLW) equation with white noise. We do not assume that the limiting equation possesses a unique equilibrium and do not impose roughness on the noise. This allows to provide the first such result in the PDE setting.