Publication: On small masses in self-similar fragmentations
On small masses in self-similar fragmentations
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Bertoin, J. (2004). On small masses in self-similar fragmentations. Stochastic Processes and Their Applications, 109(1), 13–22. https://doi.org/10.1016/j.spa.2003.08.001
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We consider a self-similar fragmentation process which preserves the total mass. We are interested in the asymptotic behavior as ε→0+ of , the number of fragments with size greater than ε 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 ϕ:]0,1[→]0,∞[ such that the limit of N(ε,t)/ϕ(ε) 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 t
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Bertoin, J. (2004). On small masses in self-similar fragmentations. Stochastic Processes and Their Applications, 109(1), 13–22. https://doi.org/10.1016/j.spa.2003.08.001