COUPLING BY REFLECTION FOR CONTROLLED DIFFUSION PROCESSES: TURNPIKE PROPERTY AND LARGE TIME BEHAVIOR OF HAMILTON-JACOBI-BELLMAN EQUATIONS

• 成果类型: Article
• 署名作者: Conforti, Giovanni
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1927
• 发表日期: 2023
• 页码: 4608-4644
• 关键词: long-time; multidimensional diffusions; contraction rates; CONVERGENCE; average

摘要

We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a proba-bilistic approach based on a variant of coupling by reflection adapted to the study of controlled diffusion processes. We prove existence and uniqueness of solutions for the ergodic Hamilton-Jacobi-Bellman equation and different kind of quantitative exponential convergence results at the level of the value function, of the optimal controls and of the optimal processes. Moreover, we provide uniform in time gradient and Hessian estimates for the solutions of the HJB equation that are of independent interest.