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

Menshikov, M.V.; Petritis, D.

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: May 15, 2014
• 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.