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Loss of mass in deterministic and random fragmentations

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  • Haas, Bénédicte

Abstract

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.

Suggested Citation

  • Haas, Bénédicte, 2003. "Loss of mass in deterministic and random fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 245-277, August.
    • Handle: RePEc:eee:spapps:v:106:y:2003:i:2:p:245-277
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    Cited by:

    1. Bertoin, Jean, 2006. "Different aspects of a random fragmentation model," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 345-369, March.
    2. Bénédicte Haas, 2007. "Fragmentation Processes with an Initial Mass Converging to Infinity," Journal of Theoretical Probability, Springer, vol. 20(4), pages 721-758, December.
    3. Cepeda, Eduardo, 2016. "Stochastic coalescence multi-fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 360-391.
    4. Bertoin, Jean, 2004. "On small masses in self-similar fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 13-22, January.
    5. Wagner Wolfgang, 2010. "Random and deterministic fragmentation models," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 399-420, January.

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