| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 54 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2021052 | |
| 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*
1
Mathematisches Institut, Universität Tübingen,
Auf der Morgenstelle 10,
72076
Tübingen, Germany.
2
School of Mathematics and Statistics, Southwest University,
Chongqing
400715, PR China.
** Corresponding author: yqwang@amss.ac.cn
Received:
29
September
2020
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.