The Annals of Applied Probability

Singularly perturbed Markov chains: Limit results and applications

George Yin and Hanqin Zhang

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 13 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1171377182

Digital Object Identifier
doi:10.1214/105051606000000682

Mathematical Reviews number (MathSciNet)
MR2292585

Zentralblatt MATH identifier
1138.60331

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

Keywords
Singular perturbation Markov chain asymptotic expansion occupation measure diffusion process

Citation

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. https://projecteuclid.org/euclid.aoap/1171377182


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