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December 2019 Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations
Ruoting Gong, Chenchen Mou, Andrzej Święch
Ann. Appl. Probab. 29(6): 3271-3310 (December 2019). DOI: 10.1214/19-AAP1473

Abstract

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.

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Ruoting Gong. Chenchen Mou. Andrzej Święch. "Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations." Ann. Appl. Probab. 29 (6) 3271 - 3310, December 2019. https://doi.org/10.1214/19-AAP1473

Information

Received: 1 September 2017; Revised: 1 August 2018; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172335
MathSciNet: MR4047981
Digital Object Identifier: 10.1214/19-AAP1473

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Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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