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.

翻译：本文研究后向半线性半线性孔径抛物线等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解线性元素法。首先,得出了连续方程解决办法的更高规律性。第二,为空间半分解得出了第一级空间精确度。第三,介绍了理论结果的理论应用对随机线性线性二次控制问题的影响。