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
| Autor: | Yanqing Wang, Andreas Prohl |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Stochastic control
Work (thermodynamics) Control and Optimization Discretization Space time MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 01 natural sciences Noise (electronics) 010101 applied mathematics Computational Mathematics Control and Systems Engineering Convergence (routing) Applied mathematics Heat equation 0101 mathematics Gradient descent Mathematics |
| Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations. 27:54 |
| ISSN: | 1262-3377 1292-8119 |
| DOI: | 10.1051/cocv/2021052 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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