Volume 27, 2021
|Number of page(s)||30|
|Published online||04 June 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*
Mathematisches Institut, Universität Tübingen,
Auf der Morgenstelle 10,
2 School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China.
** Corresponding author: firstname.lastname@example.org
Accepted: 10 May 2021
We verify strong rates of convergence for a time-implicit, finite-element based space-time discretization of the backward stochastic heat equation, and the forward-backward stochastic heat equation from stochastic optimal control. 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. This work is thus giving a theoretical foundation for the computational findings in Dunst and Prohl, SIAM J. Sci. Comput. 38 (2016) A2725–A2755.
Mathematics Subject Classification: 49J20 / 65M60 / 93E20
Key words: Strong error estimate with rates / backward stochastic heat equation / stochastic linear quadratic problem / forward-backward stochastic heat equation
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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