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
- 60G17 Sample path properties

**Résumé:** In self-similar fragmentations with a negative index, fragments
split even faster as their mass is smaller, so that the
fragmentation runs away and some mass is reduced to dust. Our
purpose is to investigate the regularity of this formation of
dust. Let $M(t)$ denote the mass of dust at time $t.\,$We give
some sufficient and some necessary conditions for the measure $dM$
to be absolutely continuous. In case of absolute continuity, we
obtain an approximation of the density by functions of small
fragments. We also study the Hausdorff dimension of the support of
$dM$ and the Hölder-continuity of the dust's mass $M$.

**Mots Clés:** *Fragmentation ; self-similarity ; loss of mass to dust ; Lebesgue density ; Hölder-continuity*

**Date:** 2003-06-11

**Prépublication numéro:** *PMA-828*