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

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**Auteur(s): **

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

- 60J25 Markov processes with continuous parameter
- 60J30 Processes with independent increments
- 82C21 Dynamic continuum models (systems of particles, etc.)

**Résumé:** We consider a linear rate equation, depending on three parameters,
that modelizes fragmentation. For each of these fragmentation
equations, there is a corresponding stochastic model, from which
we construct an explicit solution to the equation. This solution
is proved unique. We then use this solution to obtain criteria for
the presence or absence of loss of mass in the fragmentation
equation, as a function of the equation parameters. Next, we
investigate small and large times asymptotic behavior of the total
mass for a wide class of parameters. Finally, we study the loss of
mass in the stochastic models.

**Mots Clés:** *Fragmentation ; loss of mass ; subordinator ; exponential functional*

**Date:** 2002-05-27

**Prépublication numéro:** *PMA-730*

**Pdf file : **PMA-730.pdf