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| HAL : hal-00666512, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (06-02-2012) | v2 (06-06-2012) |
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| Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach |
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| Mikhail Menshikov 1Dimitri Petritis 2 |
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| (05/02/2012) |
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| 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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| 1 : | Department of Mathematics |
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University of Durham |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Théorie ergodique |
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| Domaine | : | Mathématiques/Probabilités |
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| Continuous-time Markov chain – recurrence criteria – explosion criteria – moments of passage times – implosion. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00666512, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00666512 | |
| oai:hal.archives-ouvertes.fr:hal-00666512 | |
| Contributeur : Dimitri Petritis | |
| Soumis le : Dimanche 5 Février 2012, 12:13:57 | |
| Dernière modification le : Vendredi 10 Février 2012, 09:48:28 | |
