CONVERGENCE OF A SPATIAL SEMIDISCRETIZATION FOR A BACKWARD SEMILINEAR STOCHASTIC PARABOLIC EQUATION.

This paper studies the convergence of a spatial semidiscretization for a backward semilinear stochastic parabolic equation. The fltration is general, and the spatial semidiscretization uses the standard continuous piecewise linear fnite element method. Firstly, higher regularity of the solution to the continuous equation is derived. Secondly, the frst-order spatial accuracy is derived for the spatial semidiscretization. Thirdly, an application of the theoretical results to a stochastic linear quadratic control problem is presented. [ABSTRACT FROM AUTHOR]