Higher order time discretization for the stochastic semilinear wave equation with multiplicative noise

2022/05/15 by Xiaobing Feng, Feng, Xiaobing, Akash Ashirbad Panda +3 · 3 citations
Economics, Econometrics and Finance · #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2205.07393

Abstract

In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a variational method for its error analysis and prove an improved convergence order of 3/2 for the approximates of the solution. The core of the analysis is Holder continuity in time and moment bounds for the solutions of the continuous and the discrete problem. Computational experiments are also presented.

Cited by

• Milstein-type Schemes for Hyperbolic SPDEs
• Convergence analysis for an implementable scheme to solve the linear-quadratic stochastic optimal control problem with stochastic wave equation
• Higher order numerical schemes for SPDEs with additive Noise

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