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
Keyword(s):
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 ].
2018 ◽
Vol 457
(1)
◽
pp. 776-802
2007 ◽
Vol 8
(2)
◽
pp. 261-277
◽
2016 ◽
Vol 4
(2)
◽
1994 ◽
Vol 82
(2)
◽
pp. 323-341
◽
2006 ◽
Vol 21
(2)
◽
pp. 315-341
◽