A variational formula for controlled backward stochastic partial differential equations and some application |
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Authors: | MENG Qing-xin TANG Mao-ning |
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Affiliation: | 1. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China;School of Mathematical Sciences, Fudan University, Shanghai 200433, China 2. Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China |
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Abstract: | An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established. |
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Keywords: | Variational formula stochastic evolution equation backward stochastic evolution equation stochastic maximum principle spike variation |
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