Strong law of large numbers for fragmentation processes

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 ? for 1 ≥η >0. © Association des Publications de l'Institut Henri Poincaré, 2010.