TY - JOUR
T1 - Strong law of large numbers for fragmentation processes
AU - Harris, Simon C
AU - Knobloch, Robert
AU - Kyprianou, Andreas E
PY - 2010/2
Y1 - 2010/2
N2 - 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.
AB - 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.
KW - strong law of large numbers
KW - fragmentation processes
KW - additive martingales
UR - http://www.scopus.com/inward/record.url?scp=77952556256&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1214/09-aihp311
U2 - 10.1214/09-aihp311
DO - 10.1214/09-aihp311
M3 - Article
SN - 0246-0203
VL - 46
SP - 119
EP - 134
JO - Annales de l'Institut Henri Poincaré: Probabilités et Statistiques
JF - Annales de l'Institut Henri Poincaré: Probabilités et Statistiques
IS - 1
ER -