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 proceedingChapter

1 Scopus citations

Abstract

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
Pages301-309
Number of pages9
Edition9780817683368
DOIs
StatePublished - 1 Jan 2012

Publication series

NameSystems and Control: Foundations and Applications
Number9780817683368
ISSN (Print)2324-9749
ISSN (Electronic)2324-9757

Keywords

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

Fingerprint Dive into the research topics of 'On the regularity property of Semi-Markov processes with Borel state spaces'. Together they form a unique fingerprint.

  • Cite this

    Vega-Amaya, Ó. (2012). On the regularity property of Semi-Markov processes with Borel state spaces. In Systems and Control: Foundations and Applications (9780817683368 ed., pp. 301-309). (Systems and Control: Foundations and Applications; No. 9780817683368). Birkhauser Verlag Basel. https://doi.org/10.1007/978-0-8176-8337-5_18