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| HAL : hal-00373262, version 2 |
| arXiv : 0904.0581 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (03-04-2009) | v2 (25-06-2009) |
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| A limit theorem for trees of alleles in branching processes with rare neutral mutations |
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| Jean Bertoin 1, 2 |
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| (03/04/2009) |
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| We are interested in the genealogical structure of alleles for a Bienaymé-Galton-Watson branching process with neutral mutations (infinite alleles model), in the situation where the initial population is large and the mutation rate small. We shall establish that for an appropriate regime, the process of the sizes of the allelic sub-families converges in distribution to a certain continuous state branching process (i.e. a Jirina process) in discrete time. Itô's excursion theory and the Léevy-Itô decomposition of subordinators provide fundamental insights for the results. |
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| 1 : | Département de Mathématiques et Applications (DMA) |
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CNRS : UMR8553 – Ecole Normale Supérieure de Paris - ENS Paris |
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| 2 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot |
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| Domaine | : | Mathématiques/Probabilités |
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| Weak convergence – branching process – neutral mutations – allelic partition – Lévy-Itô decomposition. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00373262, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00373262 | |
| oai:hal.archives-ouvertes.fr:hal-00373262 | |
| Contributeur : Jean Bertoin | |
| Soumis le : Jeudi 25 Juin 2009, 10:59:07 | |
| Dernière modification le : Jeudi 25 Juin 2009, 11:14:24 | |
