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

Giorgio Fabbri () and F. Russo

Working Papers from Grenoble Applied Economics Laboratory (GAEL)

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 ?-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)
JEL-codes: C02 C61 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ore
Date: 2017
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Related works:
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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