This paper studies the convergence of a spatial semidiscretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semidiscretization 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 semidiscretization. Thirdly, an application of the theoretical result to a stochastic linear quadratic control problem is presented.

翻译：本文研究后向半线性半线性半线性抛物线性方程式空间半分解的趋同。过滤是一般性的,空间半分解采用标准的连续片分线性元素法。首先,得出连续方程式解决办法的更经常性。第二,为空间半分化得出第一级空间精确度。第三,介绍了理论结果对随机线性线性二次控制问题的应用。