Stochastic maximum principle for SPDEs with noise and control on the boundary |
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Authors: | Giuseppina Guatteri |
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Affiliation: | Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy |
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Abstract: | In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problem can be interpreted as a stochastic control problem for an evolution system in a Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle. |
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Keywords: | Stochastic control Maximum principle Stochastic evolution equation Backward stochastic differential equation |
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