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 1704, AMSE Working Papers from Aix-Marseille School of Economics, France

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 dimensions; stochastic evolution equations; generalized Fukushima decomposition; stochastic optimal control in Hilbert spaces (search for similar items in EconPapers)
Pages: 19 pages
Date: 2017-01
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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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Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:1704

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