IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i3p345-369.html
   My bibliography  Save this article

Different aspects of a random fragmentation model

Author

Listed:
  • Bertoin, Jean

Abstract

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random fragmentation processes.

Suggested Citation

  • Bertoin, Jean, 2006. "Different aspects of a random fragmentation model," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 345-369, March.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:3:p:345-369
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00158-4
    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. Biggins, J. D., 1990. "The central limit theorem for the supercritical branching random walk, and related results," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 255-274, April.
    3. Liu, Quansheng, 2001. "Asymptotic properties and absolute continuity of laws stable by random weighted mean," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 83-107, September.
    4. Liu, Quansheng, 2000. "On generalized multiplicative cascades," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 263-286, April.
    5. Jagers, Peter, 1989. "General branching processes as Markov fields," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 183-212, August.
    Full references (including those not matched with items on IDEAS)

    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. Xiaoqiang Wang & Chunmao Huang, 2017. "Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 961-995, September.
    2. Gao, Zhiqiang & Liu, Quansheng, 2016. "Exact convergence rates in central limit theorems for a branching random walk with a random environment in time," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2634-2664.
    3. Bassetti, Federico & Matthes, Daniel, 2014. "Multi-dimensional smoothing transformations: Existence, regularity and stability of fixed points," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 154-198.
    4. Chen, Dayue & de Raphélis, Loïc & Hu, Yueyun, 2018. "Favorite sites of randomly biased walks on a supercritical Galton–Watson tree," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1525-1557.
    5. Yang, Hairuo, 2023. "On the law of terminal value of additive martingales in a remarkable branching stable process," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 361-376.
    6. Quansheng Liu & Emmanuel Rio & Alain Rouault, 2003. "Limit Theorems for Multiplicative Processes," Journal of Theoretical Probability, Springer, vol. 16(4), pages 971-1014, October.
    7. Caliebe, Amke & Rösler, Uwe, 2003. "Fixed points with finite variance of a smoothing transformation," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 105-129, September.
    8. Olvera-Cravioto, Mariana, 2012. "Tail behavior of solutions of linear recursions on trees," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1777-1807.
    9. Bénédicte Haas, 2007. "Fragmentation Processes with an Initial Mass Converging to Infinity," Journal of Theoretical Probability, Springer, vol. 20(4), pages 721-758, December.
    10. Decrouez, Geoffrey & Hambly, Ben & Jones, Owen Dafydd, 2015. "The Hausdorff spectrum of a class of multifractal processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1541-1568.
    11. Braunsteins, Peter & Decrouez, Geoffrey & Hautphenne, Sophie, 2019. "A pathwise approach to the extinction of branching processes with countably many types," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 713-739.
    12. Gao, Zhi-Qiang, 2018. "A second order asymptotic expansion in the local limit theorem for a simple branching random walk in Zd," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4000-4017.
    13. Buraczewski, D. & Damek, E. & Zienkiewicz, J., 2018. "Pointwise estimates for first passage times of perpetuity sequences," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2923-2951.
    14. Vincent Bansaye, 2019. "Ancestral Lineages and Limit Theorems for Branching Markov Chains in Varying Environment," Journal of Theoretical Probability, Springer, vol. 32(1), pages 249-281, March.
    15. Iksanov, Aleksander M., 2004. "Elementary fixed points of the BRW smoothing transforms with infinite number of summands," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 27-50, November.
    16. Cepeda, Eduardo, 2016. "Stochastic coalescence multi-fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 360-391.
    17. Shankar Bhamidi & Steven N. Evans & Arnab Sen, 2012. "Spectra of Large Random Trees," Journal of Theoretical Probability, Springer, vol. 25(3), pages 613-654, September.
    18. Gao, Zhi-Qiang, 2019. "Exact convergence rate in the local central limit theorem for a lattice branching random walk on Zd," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 58-66.
    19. Buraczewski, Dariusz & Damek, Ewa & Mentemeier, Sebastian & Mirek, Mariusz, 2013. "Heavy tailed solutions of multivariate smoothing transforms," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1947-1986.
    20. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.

    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:116:y:2006:i:3:p:345-369. 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.