论文标题
向后随机热方程的时空离散和随机热方程的线性季度控制问题的强大收敛速率
Strong Rates of Convergence for Space-Time Discretization of the Backward Stochastic Heat Equation, and of a Linear-Quadratic Control Problem for the Stochastic Heat Equation
论文作者
论文摘要
我们为向后的随机热方程以及从随机最佳控制的前向后随机热方程式引入了时间毫规，基于有限元素的时空离散方案，并证明了强大的收敛速率。然后将前向后的随机热方程式的完全离散的版本在梯度下降算法中使用，以大约解决由添加噪声驱动的随机热方程的线性季度控制问题。
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.
