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Discretization methods for homogeneous fragmentations


Bertoin, Jean; Rouault, A (2005). Discretization methods for homogeneous fragmentations. Journal of the London Mathematical Society , 72(1):91-109.

Abstract

Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogues of a certain type of branching random walk, which suggests the use of time-discretization to shift known results from the theory of branching random walks to the fragmentation setting. In particular, this yields interesting information about the asymptotic behaviour of fragmentations. On the other hand, homogeneous fragmentations can also be investigated using a powerful technique of discretization of space due to Kingman, namely, the theory of exchangeable partitions of N. Spatial discretization is especially well suited to the direct development for continuous times of the conceptual method of probability tilting of Lyons, Pemantle and Peres.

Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogues of a certain type of branching random walk, which suggests the use of time-discretization to shift known results from the theory of branching random walks to the fragmentation setting. In particular, this yields interesting information about the asymptotic behaviour of fragmentations. On the other hand, homogeneous fragmentations can also be investigated using a powerful technique of discretization of space due to Kingman, namely, the theory of exchangeable partitions of N. Spatial discretization is especially well suited to the direct development for continuous times of the conceptual method of probability tilting of Lyons, Pemantle and Peres.

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17 citations in Web of Science®
16 citations in Scopus®
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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
Language:English
Date:2005
Deposited On:17 Jun 2013 10:39
Last Modified:05 Apr 2016 16:49
Publisher:Oxford University Press
ISSN:0024-6107
Publisher DOI:https://doi.org/10.1112/S0024610705006423
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1077.60053
http://journals.cambridge.org/action/displayFulltext?type=1&fid=322467&jid=JLM&volumeId=72&issueId=01&aid=322466 (Publisher)

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