English

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.

Keywords

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

R2 v1 2026-06-22T01:58:04.338Z