Accelerated spatial approximations for time discretized stochastic partial differential equations

Abstract

The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations (SPDEs) defined on the whole space. Sufficient conditions are given for accelerating the convergence of the scheme with respect to the spatial approximation to higher order accuracy by an application of Richardson's method. This work extends the results of Gyöngy and Krylov [SIAM J. Math. Anal., 42 (2010), pp. 2275--2296] to schemes that discretize in time as well as space.

29 pages

References in corpus (1)

• Rate of Convergence of Space Time Approximations for stochastic evolution equations

Cited by in corpus (7)

• Finite Difference Schemes for Linear Stochastic Integro-Differential Equations
• Finite difference schemes for stochastic partial differential equations in Sobolev spaces
• Higher order spatial approximations for degenerate parabolic stochastic partial differential equations
• On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs
• Accelerated finite elements schemes for parabolic stochastic partial differential equations
• On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs
• On stochastic finite difference schemes