Strong Law of Large Numbers for Fragmentation Processes

2008/09/17 by Simon C. Harris, S. C. Harris, R. Knobloch +6
Mathematics · #60G09 #60J25 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60G09 #msc:60J25

paper · pdf · doi:10.48550/arxiv.0809.2958

arxiv created 2008/09/17 · openalex publication_date 2008/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ η>0.

Related

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• Sharp concentration for the largest and smallest fragment in a k-regular self-similar fragmentation
• Limit theorems for fragmentation processes with immigration
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