Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T20:05:25.359Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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