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arXiv · 1202.0952

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

Mikhail Menshikov·Dimitri Petritis
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Abstract

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.

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Mikhail Menshikov, Dimitri Petritis. 2012-06-14. Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach. https://doi.org/10.1016/j.spa.2014.03.001

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