Accelerated finite difference schemes for stochastic partial differential equations in the whole space

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of the solution to the Cauchy problem for linear stochastic PDEs of parabolic type can be accelerated to any given order of convergence by Richardson's method.Comment: 24 page

Accelerated spatial approximations for time discretized stochastic partial differential equations

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.Comment: 29 page