Publication details for Mikhail MenshikovMenshikov, M.V. & 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.
- Publication type: Journal Article
- ISSN/ISBN: 0304-4149 (print)
- DOI: 10.1016/j.spa.2014.03.001
- Keywords: Continuous-time Markov chain, Recurrence criteria, Explosion criteria, Moments of passage times, Implosion.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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.