On the regularity property of Semi-Markov processes with Borel state spaces

Óscar Vega-Amaya*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


This note shows that a semi-Markov process with Borel state space is regular under a fairly weak condition on the mean sojourn or holding times and assuming that the embedded Markov chain satisfies one of the following conditions: (a) it is Harris recurrent; (b) it is recurrent and the “recurrent part” of the state space is reached with probability one for every initial state; (c) it has a unique invariant probability measure. Under the latter condition, the regularity property is only ensured for almost all initial states with respect to the invariant probability measure.

Original languageEnglish
Title of host publicationSystems and Control
Subtitle of host publicationFoundations and Applications
PublisherBirkhauser Verlag Basel
Number of pages9
StatePublished - 1 Jan 2012

Publication series

NameSystems and Control: Foundations and Applications
ISSN (Print)2324-9749
ISSN (Electronic)2324-9757


  • Borel Space
  • Embed Markov Chain
  • Invariant Probability Measure
  • Markov Chain
  • Regularity Property

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