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arXiv · 0809.2958

Strong Law of Large Numbers for Fragmentation Processes

S. C. Harris·R. Knobloch·A. E. Kyprianou
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Abstract

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 $η$ for $1\geq η>0$.

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S. C. Harris, R. Knobloch, A. E. Kyprianou. 2008-09-17. Strong Law of Large Numbers for Fragmentation Processes. https://arxiv.org/abs/0809.2958

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