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 Electronic Journal of Probability > Vol. 9 (2004) > Paper 19 open journal systems 


Asymptotic Laws for Nonconservative Self-similar Fragmentations

Jean Bertoin, Université Paris VI
Alexander V. Gnedin, Rijksuniversiteit Utrecht, The Netherlands


Abstract
We consider a self-similar fragmentation process in which the generic particle of mass $x$ is replaced by the offspring particles at probability rate $x^alpha$, with positive parameter $alpha$. The total of offspring masses may be both larger or smaller than $x$ with positive probability. We show that under certain conditions the typical mass in the ensemble is of the order $t^{-1/alpha}$ and that the empirical distribution of masses converges to a random limit which we characterise in terms of the reproduction law.


Full text: PDF

Pages: 575-593

Published on: July 30, 2004
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Electronic Journal of Probability. ISSN: 1083-6489