Viscosity Solutions to Second Order Elliptic Hamilton-Jacobi-Bellman Equation with infinite delay
Optimization and Control
2021-12-28 v1 Probability
Abstract
This paper introduces a notion of viscosity solutions for second order elliptic Hamilton-Jacobi-Bellman (HJB) equations with infinite delay associated with infinite-horizon optimal control problems for stochastic differential equations with infinite delay. We identify the value functional of optimal control problems as unique viscosity solution to associated second order elliptic HJB equation with infinite delay. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
Keywords
Cite
@article{arxiv.2112.13363,
title = {Viscosity Solutions to Second Order Elliptic Hamilton-Jacobi-Bellman Equation with infinite delay},
author = {Jianjun Zhou},
journal= {arXiv preprint arXiv:2112.13363},
year = {2021}
}
Comments
39 pages. arXiv admin note: text overlap with arXiv:2009.05367, arXiv:2005.05309