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:**

- 60J30 Processes with independent increments
- 60G18 Self-similar processes

**Résumé:** Let $M_\alpha$ be the closure of the range of a stable subordinator of
index $\alpha\in ]0,1[$.
There are two natural constructions of the $M_{\alpha}$'s simultaneously for
all $\alpha\in ]0,1[$, so that
$M_{\alpha}\subseteq M_{\beta}$ for $0< \alpha < \beta <
1$: one based on the intersection of independent regenerative sets and one
based on Bochner's subordination.
We compare the corresponding two coalescent processes defined by the lengths
of complementary intervals of $[0,1]\backslash M_{1-\rho}$ for $0 < \rho < 1$.
In particular, we identify the coalescent based on the subordination scheme
with the coalescent recently introduced by Bolthausen and Sznitman.

**Mots Clés:** *fragmentation ; coalescent ; stable subordinator
*

**Date:** 1999-09-28

**Prépublication numéro:** *PMA-530*