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

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Loss of mass in deterministic and random fragmentations

Auteur(s):

Code(s) de Classification MSC:

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