Strong law of large numbers for fragmentation processes
نویسندگان
چکیده
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. Résumé. Dans l’esprit d’un résultat classique concernant les processus de Crump–Mode–Jagers, nous démontrons une loi forte des grands nombres pour des processus de fragmentation. Plus précisément, pour des processus auto-similaires de fragmentation, incluant les processus homogènes, nous prouvons la convergence presque sûre de la mesure empirique associée à la ligne d’arrêt correspondant aux premiers fragments de taille strictement plus petite qu’un η dans (0,1]. MSC: 60J25; 60G09
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