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

Mikhail Menshikov (1) , Dimitri Petritis (2)

1 Department of Mathematics
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: implosion; Continuous-time Markov chain; recurrence criteria; explosion criteria; moments of passage times; implosion.

Domaines: Probabilités [math.PR]

Mikhail Menshikov, Dimitri Petritis. Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach. 2012. ⟨hal-00666512v1⟩