Homogeneous fragmentation processes
نویسنده
چکیده
The purpose of this work is to define and study homogeneous fragmentation processes in continuous time, which are meant to describe the evolution of an object that breaks down randomly into pieces as time passes. Roughly, we show that the dynamics of such a fragmentation process are determined by some exchangeable measure on the set of partitions of �, and result from the combination of two different phenomena: a continuous erosion and sudden dislocations. In particular, we determine the class of fragmentation measures which can arise in this setting, and investigate the evolution of the size of the fragment that contains a point picked at random at the initial time. DOI: https://doi.org/10.1007/s004400100152 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-79464 Draft Version Originally published at: Bertoin, Jean (2001). Homogeneous fragmentation processes. Probability Theory and Related Fields, 212(3):301-318. DOI: https://doi.org/10.1007/s004400100152 Universités de Paris 6 & Paris 7 CNRS (UMR 7599) PRÉPUBLICATIONS DU LABORATOIRE DE PROBABILITÉS & MODÈLES ALÉATOIRES 4, place Jussieu Case 188 75 252 Paris cedex 05 http://www.proba.jussieu.fr Homogeneous fragmentation processes J. BERTOIN
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