3 research outputs found
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