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

Giorgio Fabbri (1) , Francesco Russo (2)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 UMA - Unité de Mathématiques Appliquées

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.

Mots clés: Weak Dirichlet processes in infinite dimension; Stochastic evolution equations; Generalized Fukushima decomposition; Stochastic optimal control in Hilbert spaces

Domaines: Probabilités [math.PR]

Giorgio Fabbri, Francesco Russo. HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition. 2017. ⟨hal-01447562v1⟩