Accelerated spatial approximations for time discretized stochastic partial differential equations

Details Accelerated spatial approximations for time discretized stochastic partial differential equations Accelerated spatial approximations for time discretized stochastic partial differential equations

2012-01-27

arxiv.org/abs/1201.5769v1

Mathematics

Probability

29 pages

Scientific paper

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 Gy\"ongy and Krylov [SIAM J. Math. Anal., 42 (2010), pp. 2275--2296] to schemes that discretize in time as well as space.

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