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Article Dans Une Revue Stochastic Processes and their Applications Année : 2014

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

Résumé

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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Dates et versions

hal-00666512 , version 1 (05-02-2012)
hal-00666512 , version 2 (06-06-2012)

Identifiants

Citer

Mikhail Menshikov, Dimitri Petritis. Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach. Stochastic Processes and their Applications, 2014, 124 (7), pp.2388-2414. ⟨10.1016/j.spa.2014.03.001⟩. ⟨hal-00666512v2⟩
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