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

Giorgio Fabbri () and Francesco Russo ()
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Francesco Russo: ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques appliquées

No 2017003, Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) from Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES)

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 V-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: Weak Dirichlet processes in infinite dimension; Stochastic evolution equations; Generalized Fukushima decomposition; Stochastic optimal control in Hilbert spaces (search for similar items in EconPapers)
Date: 2017-01-31
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Working Paper: HJB Equations in Infinite Dimension and Optimal Control of Stochastic Evolution Equations via Generalized Fukushima Decomposition (2017) Downloads
Working Paper: HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition (2017) Downloads
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