# 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2017
Domaine :

Littérature citée [43 références]

https://hal.archives-ouvertes.fr/hal-01447562
Contributeur : Francesco Russo <>
Soumis le : jeudi 17 août 2017 - 09:33:13
Dernière modification le : jeudi 1 février 2018 - 17:37:53

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FabbriRussoAugust2017SFB.pdf
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• HAL Id : hal-01447562, version 2
• ARXIV : 1701.07992

### Citation

Giorgio Fabbri, Francesco Russo. HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition. 2017. 〈hal-01447562v2〉

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