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:**

- 60G18 Self-similar processes
- 60J25 Markov processes with continuous parameter
- 60G09 Exchangeability

**Résumé:** We encode a certain class of stochastic fragmentation processes,
namely self-similar fragmentation processes with a negative index
of self-similarity, into a metric family tree which belongs to the
family of Continuum Random Trees of Aldous. When the splitting
times of the fragmentation are dense near 0, the tree can in turn
be encoded into a continuous height function, just as the Brownian
Continuum Random Tree is encoded in a normalized Brownian
excursion. Under mild hypotheses, we then compute the Hausdorff
dimensions of these trees, and the maximal Hölder exponents of
the height functions.

**Mots Clés:** *Self-similar fragmentation ; continuum random tree ; Hausdorff
dimension ; Hölder regularity*

**Date:** 2003-11-12

**Prépublication numéro:** *PMA-865*