scholarly journals A linear quadratic control problem for the stochastic heat equation driven by Q-Wiener processes

2018 ◽  
Vol 457 (1) ◽  
pp. 776-802
Author(s):  
Peter Benner ◽  
Christoph Trautwein
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Stochastic Heat Equation ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Wiener Processes ◽  
The Stochastic Heat Equation ◽  
Linear Quadratic Control Problem

scholarly journals 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

2021 ◽  
Author(s):  
Andreas Prohl ◽  
Yanqing Wang
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Time Discretization ◽  
Rates Of Convergence ◽  
Space Time ◽  
Stochastic Heat Equation ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
The Stochastic Heat Equation ◽  
Linear Quadratic Control Problem

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 [ 14 ].

scholarly journals A linear-quadratic control problem with discretionary stopping

2007 ◽  
Vol 8 (2) ◽  
pp. 261-277 ◽  
Author(s):  
Shigeaki Koike ◽  
◽  
Hiroaki Morimoto ◽  
Shigeru Sakaguchi ◽  
Keyword(s):  
Control Problem ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Discretionary Stopping ◽  
Linear Quadratic Control Problem
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