Temporal semi-discretizations of a backward semilinear stochastic evolution equation

06/25/2021

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by   Binjie Li, et al.

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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.