Strong Law of Large Numbers for Fragmentation Processes

Details Strong Law of Large Numbers for Fragmentation Processes Strong Law of Large Numbers for Fragmentation Processes

2008-09-17

arxiv.org/abs/0809.2958v1

Mathematics

Probability

Scientific paper

In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous 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 $1\geq \eta >0$.

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