Singularly perturbed Markov chains: Limit results and applications

• 成果类型: Article
• 署名作者: Yin, George; Zhang, Hanqin
• 署名单位: Wayne State University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000682
• 发表日期: 2007
• 页码: 207-229
• 关键词: Approximation; queues; expansions; sums

摘要

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale scenarios naturally arise. One of the important questions is: As the rate of fluctuation of the Markov chain goes to infinity, if the limit distributions of suitably centered and scaled sequences of occupation measures exist, what can be said about the convergence rate? By combining singular perturbation techniques and probabilistic methods, this paper addresses the issue by concentrating on sequences of centered and scaled functional occupation processes. The results obtained are then applied to treat a queueing system example.