IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v109y2004i1p13-22.html
   My bibliography  Save this article

On small masses in self-similar fragmentations

Author

Listed:
  • Bertoin, Jean

Abstract

We consider a self-similar fragmentation process which preserves the total mass. We are interested in the asymptotic behavior as [var epsilon]-->0+ of , the number of fragments with size greater than [var epsilon] at some fixed time t>0. Under a certain condition of regular variation type on the so-called dislocation measure, we exhibit a deterministic function [phi]:]0,1[-->]0,[infinity][ such that the limit of N([var epsilon],t)/[phi] ([var epsilon]) exists and is non-degenerate. In general the limit is random, but may be deterministic when a certain relation between the index of self-similarity and the dislocation measure holds. We also present a similar result for the total mass of fragments less than [var epsilon].

Suggested Citation

  • Bertoin, Jean, 2004. "On small masses in self-similar fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 13-22, January.
    • Handle: RePEc:eee:spapps:v:109:y:2004:i:1:p:13-22
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(03)00130-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Haas, Bénédicte, 2003. "Loss of mass in deterministic and random fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 245-277, August.
    2. Schweinsberg, Jason, 2001. "Applications of the continuous-time ballot theorem to Brownian motion and related processes," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 151-176, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Delmas, Jean-François, 2007. "Fragmentation at height associated with Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 297-311, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cepeda, Eduardo, 2016. "Stochastic coalescence multi-fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 360-391.
    2. Wagner Wolfgang, 2010. "Random and deterministic fragmentation models," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 399-420, January.
    3. Bénédicte Haas, 2007. "Fragmentation Processes with an Initial Mass Converging to Infinity," Journal of Theoretical Probability, Springer, vol. 20(4), pages 721-758, December.
    4. Bertoin, Jean, 2006. "Different aspects of a random fragmentation model," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 345-369, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:109:y:2004:i:1:p:13-22. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.