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A Note on External Uniformization for Finite Markov Chains in Continuous Time

Published online by Cambridge University Press:  27 July 2009

Masaaki Kijima
Masaaki Kijima
Affiliation:
Graduate School of Systems Management, The University of Tsukuba, Tokyo, 3-29-1 Otsuka, Bunkyo-ku Tokyo 112, Japan
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Abstract

An external uniformization technique was developed by Ross [4] to obtain approximations of transition probabilities of finite Markov chains in continuous time. Yoon and Shanthikumar [7] then reported through extensive numerical experiments that this technique performs quite well compared to other existing methods. In this paper, we show that external uniformization results from the strong law of large numbers whose underlying distributions are exponential. Based on this observation, some remarks regarding properties of the approximation are given.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 1 , January 1992 , pp. 127 - 131
Copyright
Copyright © Cambridge University Press 1992

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References

1.Keilson, J. (1979). Markov chain models-Rarity and exponentialily. New York: Springer.CrossRefGoogle Scholar
2.Kijima, M. (1987). Some results for uniformizable semi-Markov processes. Australian Journal of Statistics 29: 193–207.CrossRefGoogle Scholar
3.Kijima, M. (1989). Upper bounds of a measure of dependence and the relaxation time for finite Markov chains. Journal of Operations Research Society of Japan 32: 93–102.CrossRefGoogle Scholar
4.Ross, S.M. (1987). Approximating transition probabilities and mean occupation times in continuous-time Markov chains. Probability in the Engineering and Informational Sciences 1:251–264.CrossRefGoogle Scholar
5.Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
6.Sumita, U. & Shanthikumar, J.G. (1986). A software reliability model with multiple-error introduction and removal. IEEE Transactions on Reliability R-35: 459–462.CrossRefGoogle Scholar
7.Yoon, B.S. & Shanthikumar, J.G. (1989). Bounds and approximations for the transient behavior of continuous-time Markov chains. Probability in the Engineering and Informational Sciences 3: 175–198.CrossRefGoogle Scholar