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 \(\frac{\partial ^2 u^{{\varepsilon }}(t,x)}{\partial t^2}=\frac{\partial ^2 u^{{\varepsilon }}(t,x)}{\partial x^2}+\sqrt{{\varepsilon }}\sigma (t, x, u^{{\varepsilon }}(t,x))\dot{W}(t,x)\), where \(\dot{W}\) is white in time and fractional in space with Hurst parameter \(H\in \big (\frac{1}{4},\frac{1}{2}\big )\). The variational framework and the modified weak convergence criterion proposed by Matoussi et al. (Appl Math Optim 83(2):849–879, 2021) are adopted here.