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We establish general theorems quantifying the notion of recurrence ---through an estimation of the moments of passage times --- for irreduciblecontinuous-time Markov chains on countably infinite state spaces. Sharpconditions of occurrence of the phenomenon of explosion are also obtained. Anew phenomenon of implosion is introduced and sharp conditions for itsoccurrence are proven. The general results are illustrated by treating modelshaving a difficult behaviour even in discrete time.

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