On small masses in self-similar fragmentations

Jean Bertoin

Stochastic Processes and their Applications, 2004, vol. 109, issue 1, 13-22

Abstract: We consider a self-similar fragmentation process which preserves the total mass. We are interested in the asymptotic behavior as [var epsilon]-->0+ of , the number of fragments with size greater than [var epsilon] at some fixed time t>0. Under a certain condition of regular variation type on the so-called dislocation measure, we exhibit a deterministic function [phi]:]0,1[-->]0,[infinity][ such that the limit of N([var epsilon],t)/[phi] ([var epsilon]) exists and is non-degenerate. In general the limit is random, but may be deterministic when a certain relation between the index of self-similarity and the dislocation measure holds. We also present a similar result for the total mass of fragments less than [var epsilon].

Keywords: Fragmentation; Self-similar; Strong; limit; theorems (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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