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

2022/11/27 by Ruinan, Li, Beibei, Zhang
#60G22.} #FOS: Mathematics #MR(2010) Subject Classification}{60F10 #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.14803

Abstract

This paper is devoted to investigating Freidlin-Wentzell's large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation \frac∂² u^\e(t,x)∂ t²=\frac∂² u^\e(t,x)∂ x²+√(\e)σ(t, x, u^\e(t,x))W(t,x), where W is white in time and fractional in space with Hurst parameter H∈(\frac 14,\frac 12). The variational framework and the modified weak convergence criterion proposed by Matoussi et al. \citeMSZ are adopted here.

Related

• Large deviations for stationary measures of stochastic nonlinear wave equation with smooth white noise
• A large deviation principle for the stochastic heat equation with general rough noise
• Nonlinear stochastic wave Equation driven by rough noise
• Large deviations for a spatial average of stochastic heat and wave equations
• Moderate deviations for a stochastic wave equation in dimension three