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Self-similar fragmentations


Bertoin, Jean (2002). Self-similar fragmentations. Annales de l'Institut Henri Poincaré (B) Probabilities et Statistiques, 38(3):319-340.

Abstract

We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity , a rate of erosion c⩾0, and a so-called Lévy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation of self-similar fragmentations which enables us to reduce the study to the homogeneous case α=0 which is treated in [6].

Abstract

We introduce a probabilistic model that is meant to describe an object that falls apart randomly as time passes and fulfills a certain scaling property. We show that the distribution of such a process is determined by its index of self-similarity , a rate of erosion c⩾0, and a so-called Lévy measure that accounts for sudden dislocations. The key of the analysis is provided by a transformation of self-similar fragmentations which enables us to reduce the study to the homogeneous case α=0 which is treated in [6].

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Fragmentation; Self-similar; Exchangeable partition
Language:English
Date:2002
Deposited On:24 Jul 2013 08:13
Last Modified:07 Dec 2017 21:43
Publisher:Elsevier
ISSN:0246-0203
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/S0246-0203(00)01073-6
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1899456
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1002.60072

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