We introduce a time-implicit, finite-element based space-time discretization scheme for the backward stochastic heat equation, and for the forward-backward stochastic heat equation from stochastic optimal control, and prove strong rates of convergence. The fully discrete version of the forward-backward stochastic heat equation is then used within a gradient descent algorithm to approximately solve the linear-quadratic control problem for the stochastic heat equation driven by additive noise.

翻译：我们引入了一种时间隐含的、以空间时间为基础的空间分化计划,用于后向随机热方程式,以及由随机最佳控制产生的前向后前向随机热方程式,并证明它们具有很强的趋同率。 然后,前向后向随机热方程式的完全离散版本在梯度下行算法中被使用,以大致解决由添加噪音驱动的随机热方程式的线性赤道控制问题。