Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J25 Markov processes with continuous parameter
- 60G52 Stable processes
- 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

**Résumé:** The basic object we consider is a certain model of continuum random tree,
called the stable tree. We construct a fragmentation process
$(F^-(t),t\geq 0)$ out of this
tree by removing the vertices located under height $t$.
Thanks to a self-similarity property of the stable tree, we show that
the fragmentation process is also self-similar. The semigroup and
other features of the fragmentation are given explicitly. Asymptotic results
are given, as well as a couple of related results on continuous-state
branching processes.
As proved in a companion paper, another method for fragmenting the
stable tree induces another self-similar fragmentation with same
characteristics as the ones considered here, except for the speed at which
fragments decay.

**Mots Clés:** *Self-similar fragmentation ; stable tree ; stable processes ;
continuous-state branching process*

**Date:** 2003-02-26

**Prépublication numéro:** *PMA-796*