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

to appear
Publication type:
Paper in peer-reviewed journals
Journal:
SIAM Journal on Control and Optimization
arXiv:
images/icons/icon_arxiv.png 1701.07992
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-2100,
    author={Giorgio Fabbri and Francesco Russo },
    title={HJB equations in infinite dimension and optimal control of 
           stochastic evolution equations via generalized Fukushima 
           decomposition },
    journal={SIAM Journal on Control and Optimization },
    year={to appear },
    month={1},
}