| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Probability
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| Title: |
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Explosion, implosion, and moments of passage times for continuous-time Markov chains: a semimartingale approach |
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| Author(s): |
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Mikhail Menshikov 1, Dimitri Petritis ( ) 2 |
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| Laboratory: |
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| Research team: |
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Théorie ergodique |
| Abstract: |
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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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| Fulltext language: |
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English |
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| Production date: |
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2012-02-05 |
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| Keyword(s): |
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Continuous-time Markov chain – recurrence criteria – explosion criteria – moments of passage times – implosion. |
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| Classification: |
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60J10, 60K20 |
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| Comment: |
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33 pages |
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