Asymptotics for the small fragments of the fragmentation at nodes
Abraham, Romain ; Delmas, Jean-François
Bernoulli, Tome 13 (2007) no. 1, p. 211-228 / Harvested from Project Euclid
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We consider the fragmentation at nodes of the Lévy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic behaviour of the number of small fragments at time θ. This limit is increasing in θ and discontinuous. In the α-stable case the fragmentation is self-similar with index 1/α, with α∈(1,2), and the results are close to those Bertoin obtained for general self-similar fragmentations but with an additional assumption which is not fulfilled here.
Publié le : 2007-02-14
Classification:  continuous random tree,  fragmentation,  Lévy snake,  local time,  small fragments 
@article{1175287730,
     author = {Abraham, Romain and Delmas, Jean-Fran\c cois},
     title = {Asymptotics for the small fragments of the fragmentation at nodes},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 211-228},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175287730}
}

Abraham, Romain; Delmas, Jean-François. Asymptotics for the small fragments of the fragmentation at nodes. Bernoulli, Tome 13 (2007) no. 1, pp.  211-228. http://gdmltest.u-ga.fr/item/1175287730/