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Strong law of large numbers for fragmentation processes


Reference:

Harris, S. C., Knobloch, R. and Kyprianou, A. E., 2010. Strong law of large numbers for fragmentation processes. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 46 (1), pp. 119-134.

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    Official URL:

    http://dx.doi.org/10.1214/09-aihp311

    Abstract

    In the spirit of a classical result for Crump-Mode-Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than eta for 1 > eta > 0.

    Details

    Item Type Articles
    CreatorsHarris, S. C., Knobloch, R. and Kyprianou, A. E.
    DOI10.1214/09-aihp311
    Uncontrolled Keywordsstrong law of large numbers, fragmentation processes, additive martingales
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code21610

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