Bernoulli

  • Bernoulli
  • Volume 13, Number 1 (2007), 211-228.

Asymptotics for the small fragments of the fragmentation at nodes

Romain Abraham and Jean-François Delmas

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Abstract

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.

Article information

Source
Bernoulli Volume 13, Number 1 (2007), 211-228.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175287730

Digital Object Identifier
doi:10.3150/07-BEJ6045

Mathematical Reviews number (MathSciNet)
MR2307404

Zentralblatt MATH identifier
1134.60037

Keywords
continuous random tree fragmentation Lévy snake local time small fragments

Citation

Abraham, Romain; Delmas, Jean-François. Asymptotics for the small fragments of the fragmentation at nodes. Bernoulli 13 (2007), no. 1, 211--228. doi:10.3150/07-BEJ6045. https://projecteuclid.org/euclid.bj/1175287730


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