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On the Regularity of Skip-Free Markov Chains

Published online by Cambridge University Press:  27 July 2009

D. P. Kennedy
D. P. Kennedy
Affiliation:
Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England
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Abstract

Necessary and sufficient conditions for the regularity and recurrence of right-skip-free Markov chains are established. These generalize classical results for the case of birth-and-death processes. Expressions for the general right eigenvectors of such chains are also given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 3 , July 1994 , pp. 377 - 384
Copyright
Copyright © Cambridge University Press 1994

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References

1.Abate, J. & Whitt, W. (1989). Spectral theory for skip-free Markov chains. Probability in the Engineering and Informational Sciences 3: 77–88.CrossRefGoogle Scholar
2.Anderson, W.J. (1991). Continuous-time Markov chains. New York: Springer-Verlag.CrossRefGoogle Scholar
3.Brockwell, P.J. (1985). The extinction time of a birth, death and catastrophe process and of a related diffusion model. Advances in Applied Probability 17: 42–52.CrossRefGoogle Scholar
4.Brockwell, P.J. (1986). The extinction time of a general birth and death process with catastrophes. Journal of Applied Probability 23: 851–858.CrossRefGoogle Scholar
5.Brockwell, P.J., Gani, J., & Resnick, S.I. (1982). Birth, immigration and catastrophe processes. Advances in Applied Probability 14: 709–731.CrossRefGoogle Scholar
6.Brown, M. & Shao, Y.-S. (1987). Identifying coefficients in the spectral representation for first passage time distributions. Probability in the Engineering and Informational Sciences 1: 69–74.CrossRefGoogle Scholar
7.Dobrushin, R.L. (1952). On conditions of regularity of Markov processes which are stationary in time and have a denumerable set of possible states. Uspekhi Matematicheskikh Nauk 7(6): 185–191.Google Scholar