Loss of mass in deterministic and random fragmentations

Haas, Bénédicte

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

Journal name

Stochastic Processes and their Applications

Volume

106

Number

Publisher

Elsevier

Pages

247-277

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.

Subjects / Keywords

Exponential functional; Probabilités