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

Mikhail Menshikov (Durham University)

Frank Adams 2,

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.

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