BibTeX
@MISC{Bertoin00self-similarfragmentations,
author = {Jean Bertoin},
title = { Self-similar fragmentations},
year = {2000}
}
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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 α ∈ R, 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].
