  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.
