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| HAL : hal-00497035, version 2 |
| arXiv : 1007.0370 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (02-07-2010) | v2 (07-02-2011) |
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| Pruning Galton-Watson Trees and Tree-valued Markov Processes |
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| Romain Abraham 1Jean-Francois Delmas 2 |
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| (02/07/2010) |
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| We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process $\{ {\cal G}(u)\}$ by pruning Galton-Watson trees and an analogous process $\{{\cal G}^*(u)\}$ by pruning a critical or subcritical Galton-Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process $\{{\cal G}(u)\}$ run until its ascension time has a representation in terms of $\{{\cal G}^*(u)\}$. A similar result was obtained by Aldous and Pitman (1998) in the special case of Poisson offspring distributions where they considered uniform pruning of Galton-Watson trees by adding marks on the edges of trees. |
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| 1 : | Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO) |
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CNRS : UMR6628 – Université d'Orléans |
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| 2 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 3 : | School of Mathematical Sciences |
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Beijing Normal University / Beijing |
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| Domaine | : | Mathématiques/Probabilités |
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| Branching process – Galton-Watson process – random tree – ascension process |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00497035, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00497035 | |
| oai:hal.archives-ouvertes.fr:hal-00497035 | |
| Contributeur : Romain Abraham | |
| Soumis le : Lundi 7 Février 2011, 11:53:18 | |
| Dernière modification le : Lundi 7 Février 2011, 12:53:22 | |
