Ranked Fragmentations
ESAIM: Probability and Statistics (2010)
- Volume: 6, page 157-175
- ISSN: 1292-8100
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topBerestycki, Julien. "Ranked Fragmentations." ESAIM: Probability and Statistics 6 (2010): 157-175. <http://eudml.org/doc/104285>.
@article{Berestycki2010,
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.; exchangeable partitions; record process},
language = {eng},
month = {3},
pages = {157-175},
publisher = {EDP Sciences},
title = {Ranked Fragmentations},
url = {http://eudml.org/doc/104285},
volume = {6},
year = {2010},
}
TY - JOUR
AU - Berestycki, Julien
TI - Ranked Fragmentations
JO - ESAIM: Probability and Statistics
DA - 2010/3//
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.; exchangeable partitions; record process
UR - http://eudml.org/doc/104285
ER -
References
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