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2014 Stochastic Perron's method for optimal control problems with state constraints
Dmitry Rokhlin
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Electron. Commun. Probab. 19: 1-15 (2014). DOI: 10.1214/ECP.v19-3616

Abstract

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.

Citation

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Dmitry Rokhlin. "Stochastic Perron's method for optimal control problems with state constraints." Electron. Commun. Probab. 19 1 - 15, 2014. https://doi.org/10.1214/ECP.v19-3616

Information

Accepted: 20 October 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1310.93085
MathSciNet: MR3274519
Digital Object Identifier: 10.1214/ECP.v19-3616

Subjects:
Primary: 93E20
Secondary: 49L25, 60H30

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