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Accelerated finite difference schemes for linear stochastic partial differential equations in the whole space. (English) Zbl 1222.65009
Authors’ abstract: 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 partial differential equations of parabolic type can be accelerated to any given order of convergence by Richardson’s method.

MSC:
65C30Stochastic differential and integral equations
65M06Finite difference methods (IVP of PDE)
60H15Stochastic partial differential equations
65B05Extrapolation to the limit, deferred corrections
35R10Partial functional-differential equations
60H35Computational methods for stochastic equations
65M12Stability and convergence of numerical methods (IVP of PDE)