# 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
HAL:
arXiv:
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},
}