Temporal semi-discretizations of a backward semilinear stochastic evolution equation

Abstract

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.