VISCOSITY SOLUTIONS TO SECOND ORDER ELLIPTIC HAMILTON-JACOBI-BELLMAN EQUATIONS WITH INFINITE DELAY

• 成果类型: Article
• 署名作者: Zhou, Jianjun
• 署名单位: Northwest A&F University - China
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2078
• 发表日期: 2024
• 页码: 4709-4757
• 关键词: path-dependent pdes; optimal stochastic-control; differential-equations; diffusion-processes; HJB equations; dimensions; uniqueness

摘要

This paper introduces a notion of viscosity solutions for second order elated with infinite-horizon optimal control problems for stochastic differential equations with infinite delay. We identify the value functional of optimal control problems as unique viscosity solution to associated second order elliptic HJB equations with infinite delay. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.