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Ranked Fragmentations

Published online by Cambridge University Press:  15 November 2002

Julien Berestycki
Julien Berestycki*
Affiliation:
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.
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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.

Keywords

Fragmentationself-similarsubordinatorexchangeable partitionsrecord process.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 157 - 175
Copyright
© EDP Sciences, SMAI, 2002

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