Menshikov, M.V. and 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). pp. 2388-2414.
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.
| Item Type: | Article |
|---|---|
| Keywords: | Continuous-time Markov chain, Recurrence criteria, Explosion criteria, Moments of passage times, Implosion. |
| Full text: | (NA) Not Applicable Download PDF (arXiv version) (308Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | http://dx.doi.org/10.1016/j.spa.2014.03.001 |
| Publisher statement: | NOTICE: this is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and their Applications, 124, 7, 2014, 10.1016/j.spa.2014.03.001. |
| Date accepted: | 03 March 2014 |
| Date deposited: | No date available |
| Date of first online publication: | 12 March 2014 |
| Date first made open access: | No date available |
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