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
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