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

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

2012-02-05

arxiv.org/abs/1202.0952v1

Mathematics

Probability

33 pages

Scientific paper

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.

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