HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition
june, 2017
Publication type:
Paper in peer-reviewed journals
Journal:
SIAM Journal on Control and Optimization, vol. 55(6), pp. 4072–4091
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Keywords :
Weak Dirichlet processes in infinite dimension; Stochastic evolution equations; Generalized Fukushima decomposition; Stochastic optimal control in Hilbert spaces.
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.
BibTeX:
@article{Fab-Rus-2017-1, author={Giorgio Fabbri and Francesco Russo }, title={HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition }, doi={10.1137/17M1113801 }, journal={SIAM Journal on Control and Optimization }, year={2017 }, month={6}, volume={55(6) }, pages={4072–4091}, }