The Annals of Applied Probability

Singularly perturbed Markov chains: Limit results and applications

George Yin and Hanqin Zhang

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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.

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Ann. Appl. Probab., Volume 17, Number 1 (2007), 207-229.

First available in Project Euclid: 13 February 2007

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Zentralblatt MATH identifier

Primary: 34E05: Asymptotic expansions 60F17: Functional limit theorems; invariance principles 60J27: Continuous-time Markov processes on discrete state spaces

Singular perturbation Markov chain asymptotic expansion occupation measure diffusion process


Yin, George; Zhang, Hanqin. Singularly perturbed Markov chains: Limit results and applications. Ann. Appl. Probab. 17 (2007), no. 1, 207--229. doi:10.1214/105051606000000682.

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