Strong law of large numbers for fragmentation processes
Harris, S. C. ; Knobloch, R. ; Kyprianou, A. E.
Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, p. 119-134 / Harvested from Project Euclid
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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.
Publié le : 2010-02-15
Classification:  Fragmentation processes,  Strong law of large numbers,  Additive martingales,  60J25,  60G09 
@article{1267454111,
     author = {Harris, S. C. and Knobloch, R. and Kyprianou, A. E.},
     title = {Strong law of large numbers for fragmentation processes},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {46},
     number = {1},
     year = {2010},
     pages = { 119-134},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1267454111}
}

Harris, S. C.; Knobloch, R.; Kyprianou, A. E. Strong law of large numbers for fragmentation processes. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp.  119-134. http://gdmltest.u-ga.fr/item/1267454111/