Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

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

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

Save or Share this output

Export:
Export
Look up in GoogleScholar