Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 73, 15 pp.
Stochastic Perron's method for optimal control problems with state constraints
We apply the stochastic Perron method of Bayraktar and Sîrbu to a general infinite horizon optimal control problem, where the state $X$ is a controlled diffusion process, and the state constraint is described by a closed set. We prove that the value function $v$ is bounded from below (resp., from above) by a viscosity supersolution (resp., subsolution) of the related state constrained problem for the Hamilton-Jacobi-Bellman equation. In the case of a smooth domain, under some additional assumptions, these estimates allow to identify $v$ with a unique continuous constrained viscosity solution of this equation.
Electron. Commun. Probab., Volume 19 (2014), paper no. 73, 15 pp.
Accepted: 20 October 2014
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 93E20: Optimal stochastic control
Secondary: 49L25: Viscosity solutions 60H30: Applications of stochastic analysis (to PDE, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
Rokhlin, Dmitry. Stochastic Perron's method for optimal control problems with state constraints. Electron. Commun. Probab. 19 (2014), paper no. 73, 15 pp. doi:10.1214/ECP.v19-3616. https://projecteuclid.org/euclid.ecp/1465316775