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Convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation (2105.10130v7)
Published 21 May 2021 in math.NA and cs.NA
Abstract: This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discretization uses the standard continuous piecewise linear element method. Firstly, higher regularity of the solution to the continuous equation is derived. Secondly, the first-order spatial accuracy is derived for the spatial semi-discretization. Thirdly, an application of the theoretical result to a stochastic linear quadratic control problem is presented.