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Issue ESAIM: PS
Volume 6, 2002
Page(s) 157 - 175
DOI 10.1051/ps:2002009



ESAIM: P&S, July 2002, Vol. 6, pp. 157-175
DOI: 10.1051/ps:2002009

Ranked Fragmentations

Julien Berestycki

Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, UMR 7599 du CNRS, 175 rue du Chevaleret, 75013 Paris, France; jberest@ccr.jussieu.fr.

(Received October 30, 2001. Revised March 28, 2002.)

Abstract
In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study the small-time behavior of a ranked fragmentation.


Mathematics Subject Classification. 60J25, 60G09.

Key words: Fragmentation, self-similar, subordinator, exchangeable partitions, record process.


© EDP Sciences, SMAI 2002


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