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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.
- Source :
- ESAIM: Control, Optimisation & Calculus of Variations; 6/4/2021, Vol. 26, p1-30, 30p
- Publication Year :
- 2021
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- STOCHASTIC control theory
HEAT equation
SPACETIME
Subjects
Details
- Language :
- English
- ISSN :
- 12928119
- Volume :
- 26
- Database :
- Complementary Index
- Journal :
- ESAIM: Control, Optimisation & Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 150876504
- Full Text :
- https://doi.org/10.1051/cocv/2021052