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Stochastic Perron's method for optimal control problems with state constraints

   
@article{ECP3616,
	author = {Dmitry Rokhlin},
	title = {Stochastic Perron's method for optimal control problems with state constraints},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {Stochastic Perron's method; State constraints; Viscosity solution; Comparison result},
	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.},
	pages = {no. 73, 1-15},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3616},    
        url = {http://ecp.ejpecp.org/article/view/3616}}