| Abstrakt: |
We propose a time-implicit, finite-element-based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear noise of type |$[X(t)+\sigma (t)]\,\,\textrm{d}W(t)$| and prove optimal convergence w.r.t. both space and time discretization parameters. In particular, we employ the stochastic Riccati equation as a proper analytical tool to handle the linear noise, and thus extend the applicability of the earlier work by Prohl & Wang (2021, 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. ESAIM Control Optim. Calc. Var. , 27 , 54), where the error analysis was restricted to additive noise. [ABSTRACT FROM AUTHOR] |
