| Issue |
ESAIM: PS
Volume 6, 2002
|
|
|---|---|---|
| Page(s) | 157 - 175 | |
| DOI | https://doi.org/10.1051/ps:2002009 | |
| Published online | 15 November 2002 | |
Ranked Fragmentations
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:
30
October
2001
Revised:
28
March
2002
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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