Strong rates of convergence for a space-time discretization of the backward stochastic heat equation, and of a linear-quadratic control problem for the stochastic heat equation

We verify strong rates of convergence for a time-implicit, finite-element based space-time discretization the backward stochastic heat equation, and forward-backward equation from optimal control. The fully discrete version is then used within gradient descent algorithm to approximately solve linear-quadratic control problem driven by additive noise. This work thus giving theoretical foundation computational findings in Dunst Prohl, SIAM J. Sci. Comput. 38 (2016) A2725–A2755.