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Conditions for integrability of Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

K. Hamza  and
F. C. Klebaner
K. Hamza*
Affiliation:
The University of Melbourne
F. C. Klebaner*
Affiliation:
The University of Melbourne
*
∗Postal address for both authors: Department of Statistics, The University of Melbourne, Parkville, VIC 3052, Australia.
∗Postal address for both authors: Department of Statistics, The University of Melbourne, Parkville, VIC 3052, Australia.
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Abstract

We give simple sufficient conditions for integrability of continuous-time Markov chains in terms of their infinitesimal parameters. Similar conditions for regularity are stated first, and a simple proof given.

Keywords

CONTINUOUS-TIME MARKOV CHAINSREGULARITY

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J75: Jump processes 60J25: Continuous-time Markov processes on general state spaces
Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 541 - 547
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by the Australian Research Council.

References

[1] Chen, Mu-Fa (1991) On three classical problems for Markov chains with continuous time parameters. J. Appl. Prob. 28, 305–320.CrossRefGoogle Scholar
[2] Chung, K. L. (1967) Markov Chains with Stationary Transition Probabilities. Springer-Verlag, New York.Google Scholar
[3] Dellacherie, C. and Meyer, P. (1982) Probabilities and Potential B. North-Holland, Amsterdam.Google Scholar
[4] Ethier, S. and Kurtz, T. (1986) Markov Processes, Characterization and Convergence. Wiley, New York.CrossRefGoogle Scholar
[5] Jacod, J. and Shiryaev, A. N. (1987) Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar