Semilinear stochastic partial differential equations: Central limit theorem and moderate deviations

Abstract

In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to stochastic partial differential equations of various types such as the stochastic Burgers equation and the reaction‐diffusion equations perturbed by space‐time white noise. The Garsia lemma is crucial to our results.