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Temporal semi-discretizations of a backward semilinear stochastic evolution equation (2106.13428v3)
Published 25 Jun 2021 in math.NA, cs.NA, math.OC, and math.PR
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 the first two temporal semi-discretizations is established, and an explicit convergence rate is derived for the third temporal semi-discretization. The third temporal semi-discretization is applied to a general stochastic linear quadratic control problem, and the convergence of a temporally semi-discrete approximation to the optimal control is established.