Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise
Optimization and Control
2020-12-09 v1 Numerical Analysis
Numerical Analysis
Abstract
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 , 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 [16], where the error analysis was restricted to additive noise.
Keywords
Cite
@article{arxiv.2012.04418,
title = {Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise},
author = {Andreas Prohl and Yanqing Wang},
journal= {arXiv preprint arXiv:2012.04418},
year = {2020}
}