2014/05/16 by Dmitry B. Rokhlin, Rokhlin, Dmitry B.
Economics, Econometrics and Finance · Mathematics · #49L25 #60H30 #93E20 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:49L25 #msc:60H30 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1405.4252
14 pages
openalex publication_date 2014/05/16 · arxiv created 2014/09/24 · arxiv updated 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.