The Large Deviation of Semilinear Stochastic Partial Differential Equation Driven by Brownian Sheet

TL;DR

This paper establishes a large deviation principle for one-dimensional semilinear stochastic PDEs driven by nonlinear multiplicative noise, using energy estimates, approximation, and weak convergence methods.

Contribution

It introduces a novel approach to proving LDP for semilinear SPDEs with nonlinear noise, expanding the theoretical understanding of their probabilistic behavior.

Findings

Proved existence of global solutions for the SPDEs.

Established the large deviation principle for the solutions.

Applied weak convergence method to derive LDP.

Abstract

We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation procedure, we obtain the existence of global solution. Then the large deviation principle is obtained via weak convergence method.