Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Spaces
Probability
2020-09-14 v1 Optimization and Control
Abstract
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic evolution equations in Hilbert spaces. 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.2009.05367,
title = {Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Spaces},
author = {Jianjun Zhou},
journal= {arXiv preprint arXiv:2009.05367},
year = {2020}
}
Comments
50 pages. arXiv admin note: substantial text overlap with arXiv:2005.05309, arXiv:2007.04079; text overlap with arXiv:2004.02095