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Loss of mass in deterministic and random fragmentations

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Date
2003
Dewey
Probabilités et mathématiques appliquées
Sujet
Exponential functional; Probabilités
Journal issue
Stochastic Processes and their Applications
Volume
106
Number
2
Publication date
08-2003
Article pages
247-277
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/S0304-4149(03)00045-0
URI
https://basepub.dauphine.fr/handle/123456789/1989
Collections
  • CEREMADE : Publications
Metadata
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Author
Haas, Bénédicte
Type
Article accepté pour publication ou publié
Abstract (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.

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