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.

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