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.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01447562
Contributeur : Francesco Russo <>
Soumis le : vendredi 27 janvier 2017 - 07:43:49
Dernière modification le : jeudi 23 février 2017 - 01:09:44

Fichiers

controllo25January2017ToSubmit...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01447562, version 1
  • 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-01447562>

Partager

Métriques

Consultations de
la notice

61

Téléchargements du document

32