Strong Law of Large Numbers for Fragmentation Processes

Harris, S. C.; Knobloch, R.; Kyprianou, A. E.

Strong Law of Large Numbers for Fragmentation Processes

Authors

Harris, S. C.

Knobloch, R.

Kyprianou, A. E.

Description

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 $1\geq η>0$.