Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 68, Issue 2, Pages 181-217Publisher
SPRINGER
DOI: 10.1007/s00245-013-9203-7
Keywords
Stochastic maximum principle; Stochastic partial differential equation; Optimal control; Adjoint process
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We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form that allows direct applications to a large class of controlled stochastic parabolic equations. We allow for a diffusion coefficient dependent on the control parameter, and the space of control actions is general, so that in particular we need to introduce two adjoint processes. The second adjoint process takes values in a suitable space of operators on L (4).
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