STOCHASTIC REPRESENTATIONS FOR SOLUTIONS TO PARABOLIC DIRICHLET PROBLEMS FOR NONLOCAL BELLMAN EQUATIONS

We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton–Jacobi–Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated...

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Bibliographic Details
Published in:The Annals of applied probability 2019-12, Vol.29 (6), p.3271-3310
Main Authors: Gong, Ruoting, Mou, Chenchen, Święch, Andrzej
Format: Article
Language:English
Subjects:
Boundary value problems
Dirichlet problem
Dynamic programming
Optimal control
Partial differential equations
Representations
Stochastic models
Viscosity
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Summary:We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton–Jacobi–Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
ISSN:1050-5164
2168-8737
DOI:10.1214/19-AAP1473