A large deviation principle for nonlinear stochastic wave equation driven by rough noise

Abstract

This paper is devoted to investigating Freidlin-Wentzell's large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation $\frac{\partial^2 u^{\e}(t,x)}{\partial t^2}=\frac{\partial^2 u^{\e}(t,x)}{\partial x^2}+\sqrt{\e}σ(t, x, u^{\e}(t,x))\dot{W}(t,x)$, where $\dot{W}$ is white in time and fractional in space with Hurst parameter $H\in (\frac{1}{4},\frac{1}{2})$. The variational framework and the modified weak convergence criterion proposed by Matoussi et al. \cite{MSZ} are adopted here.

arXiv admin note: substantial text overlap with arXiv:2205.13157 by other authors