Viscosity Solutions to First Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Space
Probability
2020-07-09 v1 Optimization and Control
Abstract
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
Cite
@article{arxiv.2007.04079,
title = {Viscosity Solutions to First Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Space},
author = {Jianjun Zhou},
journal= {arXiv preprint arXiv:2007.04079},
year = {2020}
}
Comments
25 pages. arXiv admin note: substantial text overlap with arXiv:2005.05309, arXiv:2004.02095