Verification by stochastic Perron's method in stochastic exit time control problems
Optimization and Control
2013-11-01 v1 Probability
Abstract
We apply the Stochastic Perron method, created by Bayraktar and S\^irbu, to a stochastic exit time control problem. Our main assumption is the validity of the Strong Comparison Result for the related Hamilton-Jacobi-Bellman (HJB) equation. Without relying on Bellman's optimality principle we prove that inside the domain the value function is continuous and coincides with a viscosity solution of the Dirichlet boundary value problem for the HJB equation.
Cite
@article{arxiv.1310.8411,
title = {Verification by stochastic Perron's method in stochastic exit time control problems},
author = {Dmitry B. Rokhlin},
journal= {arXiv preprint arXiv:1310.8411},
year = {2013}
}
Comments
14 pages