# HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition

Abstract : A stochastic optimal control problem driven by an abstract evolution equation in a separable Hilbert space is considered. Thanks to the identification of the mild solution of the state equation as $\nu$-weak Dirichlet process, the value processes is proved to be a real weak Dirichlet process. The uniqueness of the corresponding decomposition is used to prove a verification theorem. Through that technique several of the required assumptions are milder than those employed in previous contributions about non-regular solutions of Hamilton-Jacobi-Bellman equations.
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.4072-4091
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https://hal.archives-ouvertes.fr/hal-01447562
Contributeur : Francesco Russo <>
Soumis le : jeudi 17 août 2017 - 09:33:13
Dernière modification le : lundi 24 septembre 2018 - 12:45:58

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• HAL Id : hal-01447562, version 2

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Giorgio Fabbri, Francesco Russo. HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.4072-4091. 〈hal-01447562v2〉

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