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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Menshikov, Mikhail¹  Petritis, Dimitri² 

[1] Univ Durham, Dept Math Sci, Durham DHI 3LE, England

[2] Univ Rennes 1, Inst Rech Math, F-35042 Rennes, France

关键词: Continuous-time Markov chain;    Recurrence criteria;    Explosion criteria;    Moments of passage times;    Implosion;   

DOI  :  10.1016/j.spa.2014.03.001

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free