Mikhail Menshikov, Dimitri Petritis
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.
View original:
http://arxiv.org/abs/1202.0952
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