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Regularity conditions for semi-Markov and Markov chains in continuous time

Published online by Cambridge University Press:  14 July 2016

Russell Gerrard
Russell Gerrard*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

The classical condition for regularity of a Markov chain is extended to include semi-Markov chains. In addition, for any given semi-Markov chain, we find Markov chains which exhibit identical regularity properties. This is done either (i) by transforming the state space or, alternatively, (ii) by imposing conditions on the holding-time distributions. Brief consideration is given to the problem of extending the results to processes other than semi-Markov chains.

Keywords

SEMI-MARKOV CHAINREGULARITYEXPLOSION
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 505 - 512
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This work was supported by the SERC.

References

[1] Feller, W. (1957) On boundaries and lateral conditions for the Kolmogorov differential equations. Ann. Math. 65, 527–570.Google Scholar
[2] Feller, W. (1964) On semi-Markov processes. Proc. Nat. Acad. Sci. U.S.A. 51, 653–659.Google Scholar
[3] Freedman, D. (1971) Markov Chains. Holden-Day, San Francisco.Google Scholar
[4] Loève, M. (1960) Probability Theory, 2nd edn. Van Nostrand, Princeton, NJ.Google Scholar
[5] Pyke, R. W. (1961) Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32, 1231–1242.Google Scholar