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Article Dans Une Revue Applied Mathematics and Optimization Année : 2013

Stochastic maximum principle for optimal control of SPDEs

Résumé

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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Dates et versions

hal-00783615 , version 1 (01-02-2013)

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Marco Fuhrman, Ying Hu, Gianmario Tessitore. Stochastic maximum principle for optimal control of SPDEs. Applied Mathematics and Optimization, 2013, 68 (2), pp.181-217. ⟨10.1007/s00245-013-9203-7⟩. ⟨hal-00783615⟩
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