HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Control and Optimization Year : 2017

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

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 $\nu$-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.
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Dates and versions

hal-01447562 , version 1 (27-01-2017)
hal-01447562 , version 2 (17-08-2017)

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Cite

Giorgio Fabbri, Francesco Russo. HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition. SIAM Journal on Control and Optimization, 2017, 55 (6), pp.4072-4091. ⟨10.1137/17M1113801⟩. ⟨hal-01447562v2⟩
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