378 articles – 175 references  [version française]
 HAL: hal-00497035, version 2
 arXiv: 1007.0370
 DOI: 10.1214/11-AIHP423
 Pruning Galton-Watson Trees and Tree-valued Markov ProcessesAbraham R., Delmas J.-F., He H.Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 48, 3 (2012) 688-705 - http://hal.archives-ouvertes.fr/hal-00497035
 Available versions: v1 (2010-07-02) v2 (2011-02-07)
Article in peer-reviewed journal
Mathematics/Probability
Pruning Galton-Watson Trees and Tree-valued Markov Processes
Romain Abraham () 1, Jean-François Delmas (, ) 2, Hui He 1, 3
 1: Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) http://www.univ-orleans.fr/mapmo/ Université d'Orléans – CNRS : UMR7349 Fédération Denis Poisson, Bâtiment de Mathématiques, B.P. 6759, 45067 Orléans cedex 2 France 2: Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) http://cermics.enpc.fr/ Ecole des Ponts ParisTech 6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2 France 3: School of Mathematical Sciences Beijing Normal University / Beijing Beijing Normal University, Beijing 100875, P.R.China China
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.
English
2010-07-02

 Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Publisher Institute Henri Poincaré ISSN 0246-0203
international
2012
48
3
688-705

Branching process – Galton-Watson process – random tree – ascension process
05C05, 60J80, 60J27

 Project Id ANR-08-BLAN-0190
Attached file list to this document:
 TEX
 GW_final.tex(54.8 KB)
 PDF
 GW_final.pdf(200.9 KB)
 PS
 GW_final.ps(708 KB)
 hal-00497035, version 2 http://hal.archives-ouvertes.fr/hal-00497035 oai:hal.archives-ouvertes.fr:hal-00497035 From: Romain Abraham <> Submitted on: Monday, 7 February 2011 11:53:18 Updated on: Wednesday, 27 June 2012 14:52:37