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

• 成果类型: Article
• 署名作者: Gong, Ruoting; Mou, Chenchen; Swiech, Andrzej
• 署名单位: Illinois Institute of Technology; University of California System; University of California Los Angeles; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1473
• 发表日期: 2019
• 页码: 3271-3310
• 关键词: viscosity solutions; differential-equations; Levy processes; EXISTENCE; formulas; state; games

摘要

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.