Explosion, implosion, and moments of passage times for continuous-time   Markov chains: a semimartingale approach
  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. 
Mikhail Menshikov and Dimitri Petritis
math.PR math-ph math.MP