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Explosion, implosion, and moments of passage times for continuous-time Markov chains: A semimartingale approach

Menshikov, M.V.; Petritis, D.

Authors

D. Petritis



Abstract

We establish general theorems quantifying the notion of recurrence–through an estimation of the moments of passage times–for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of occurrence of the phenomenon of explosion are also obtained. A new phenomenon of implosion is introduced and sharp conditions for its occurrence are proven. The general results are illustrated by treating models having a difficult behaviour even in discrete time.

Citation

Menshikov, M., & Petritis, D. (2014). Explosion, implosion, and moments of passage times for continuous-time Markov chains: A semimartingale approach. Stochastic Processes and their Applications, 124(7), 2388-2414. https://doi.org/10.1016/j.spa.2014.03.001

Journal Article Type Article
Acceptance Date Mar 3, 2014
Online Publication Date Mar 12, 2014
Publication Date Jul 1, 2014
Deposit Date May 13, 2014
Publicly Available Date Mar 28, 2024
Journal Stochastic Processes and their Applications
Print ISSN 0304-4149
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 124
Issue 7
Pages 2388-2414
DOI https://doi.org/10.1016/j.spa.2014.03.001
Keywords Continuous-time Markov chain, Recurrence criteria, Explosion criteria, Moments of passage times, Implosion.

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