On the genealogy of conditioned stable Lévy forests

Abstract : We give a realization of the stable Lévy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent Galton-Watson trees whose offspring distribution is in the domain of attraction of any stable law conditioned on their total progeny to be equal to $n$. We prove that when $n$ and $k$ tend towards $+\infty$, under suitable rescaling, the associated coding random walk, the contour and height processes converge in law on the Skorokhod space respectively towards the "first passage bridge" of a stable Lévy process with no negative jumps and its height process.
Type de document :
Pré-publication, Document de travail
2007
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https://hal.archives-ouvertes.fr/hal-00155592
Contributeur : Juan Carlos Pardo Millan <>
Soumis le : lundi 18 juin 2007 - 16:10:58
Dernière modification le : vendredi 16 novembre 2018 - 01:55:27
Document(s) archivé(s) le : jeudi 8 avril 2010 - 18:00:06

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  • HAL Id : hal-00155592, version 1
  • ARXIV : 0706.2605

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Loic Chaumont, Juan Carlos Pardo Millan. On the genealogy of conditioned stable Lévy forests. 2007. 〈hal-00155592〉

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