Ranked fragmentations

Julien Berestycki

ESAIM: Probability and Statistics (2002)

  • Volume: 6, page 157-175
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Berestycki, Julien. "Ranked fragmentations." ESAIM: Probability and Statistics 6 (2002): 157-175. <http://eudml.org/doc/245516>.

@article{Berestycki2002,
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.},
author = {Berestycki, Julien},
journal = {ESAIM: Probability and Statistics},
keywords = {fragmentation; self-similar; subordinator; exchangeable partitions; record process},
language = {eng},
pages = {157-175},
publisher = {EDP-Sciences},
title = {Ranked fragmentations},
url = {http://eudml.org/doc/245516},
volume = {6},
year = {2002},
}

TY - JOUR
AU - Berestycki, Julien
TI - Ranked fragmentations
JO - ESAIM: Probability and Statistics
PY - 2002
PB - EDP-Sciences
VL - 6
SP - 157
EP - 175
AB - 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.
LA - eng
KW - fragmentation; self-similar; subordinator; exchangeable partitions; record process
UR - http://eudml.org/doc/245516
ER -

References

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