@article{EJP215,
author = {Jean Bertoin and Alexander Gnedin},
title = {Asymptotic Laws for Nonconservative Self-similar Fragmentations},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {9},
year = {2004},
keywords = {},
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.},
pages = {no. 19, 575-593},
issn = {1083-6489},
doi = {10.1214/EJP.v9-215},
url = {http://ejp.ejpecp.org/article/view/215}}