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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

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