Strong law of large numbers for fragmentation processes

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

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 1, page 119-134
  • ISSN: 0246-0203

Abstract

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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 η for 1≥η>0.

How to cite

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Harris, S. C., Knobloch, R., and Kyprianou, A. E.. "Strong law of large numbers for fragmentation processes." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 119-134. <http://eudml.org/doc/241649>.

@article{Harris2010,
abstract = {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 η for 1≥η&gt;0.},
author = {Harris, S. C., Knobloch, R., Kyprianou, A. E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fragmentation processes; strong law of large numbers; additive martingales},
language = {eng},
number = {1},
pages = {119-134},
publisher = {Gauthier-Villars},
title = {Strong law of large numbers for fragmentation processes},
url = {http://eudml.org/doc/241649},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Harris, S. C.
AU - Knobloch, R.
AU - Kyprianou, A. E.
TI - Strong law of large numbers for fragmentation processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 119
EP - 134
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 η for 1≥η&gt;0.
LA - eng
KW - fragmentation processes; strong law of large numbers; additive martingales
UR - http://eudml.org/doc/241649
ER -

References

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