Large Deviation Principle for Singularly Perturbed Stochastic Damped Wave Equations

Abstract

A large deviation principle is built for the following singularly perturbed stochastic nonlinear damped wave equations on bounded regular domains: We use a weak convergence method. The small parameter ν parametrises both the strength of noise and the singular perturbation. The rate function of large deviations is proven to be that of the large deviations for the stochastic heat equation This result shows the effectiveness of asymptotic approximation of the stochastic heat equation to singularly perturbed stochastic wave equations.