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| HAL: hal-00141154, version 2 |
| arXiv: 0704.1475 |
| Detailed view |  Export this paper |
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| Stochastic Processes and their Applications 119 (2008) 1124-1143 |
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| Available versions: | v1 (2007-04-11) | v2 (2009-03-24) |
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| Williams' decomposition of the Lévy continuous random tree and simultaneous extinction probability for populations with neutral mutations |
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| Romain Abraham 1Jean-François Delmas 2 |
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| (2008) |
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| We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as an immigration process with intensity proportional to the size of the population. First we establish a Williams' decomposition of the genealogy of the total population given by a continuous random tree, according to the ancestral lineage of the last individual alive. This allows us give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population. |
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| 1: | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| 2: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/Probability |
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| continuous state branching process – immigration – continuous random tree – Williams' decomposition – probability of extinction – neutral mutation |
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| hal-00141154, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00141154 | |
| oai:hal.archives-ouvertes.fr:hal-00141154 | |
| From: Jean-François Delmas | |
| Submitted on: Tuesday, 24 March 2009 11:08:15 | |
| Updated on: Tuesday, 24 March 2009 11:28:12 | |
