Strong law of large numbers for fragmentation processes

Simon C Harris, Robert Knobloch, Andreas E Kyprianou

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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.
Original languageEnglish
Pages (from-to)119-134
Number of pages16
JournalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
Issue number1
Publication statusPublished - Feb 2010


  • strong law of large numbers
  • fragmentation processes
  • additive martingales


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