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Loss of mass in deterministic and random fragmentations

Haas, Bénédicte (2003), Loss of mass in deterministic and random fragmentations, Stochastic Processes and their Applications, 106, 2, p. 247-277. http://dx.doi.org/10.1016/S0304-4149(03)00045-0

Type
Article accepté pour publication ou publié
Date
2003
Nom de la revue
Stochastic Processes and their Applications
Volume
106
Numéro
2
Éditeur
Elsevier
Pages
247-277
Identifiant publication
Métadonnées
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Auteur(s)
Haas, Bénédicte
Résumé (EN)
We consider a linear rate equation, depending on three parameters, that model 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
Exponential functional; Probabilités