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

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)
Date: 2017
New Economics Papers: this item is included in nep-ore
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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)
Working Paper: HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition (2017)
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