This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and general coefficient with Lipschitz continuity, the convergence of three Euler type temporal semi-discretizations is established without regularity assumption on the solution. Moreover, the third temporal semi-discretization is applied to a stochastic linear quadratic control problem, and an explicit convergence rate is derived.

翻译：本文研究了后向半线性半线性进化方程式三种时间半分解的趋同情况。对于与Lipschitz连续性的一般终点值和一般系数而言,三种Euler型暂时半分解的趋同情况是在没有定期假定解决办法的情况下确定的。此外,第三个时间半分解适用于蒸汽线性线性二次曲线控制问题,并得出了明确的趋同率。