Strong law of large numbers for fragmentation processes

Simon C Harris; Robert Knobloch; Andreas E Kyprianou

doi:10.1214/09-aihp311

Strong law of large numbers for fragmentation processes

Simon C Harris
, Robert Knobloch
, Andreas E Kyprianou

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

194 Downloads (Pure)

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 eta for 1 > eta > 0.

Original language	English
Pages (from-to)	119-134
Number of pages	16
Journal	Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Volume	46
Issue number	1
DOIs	https://doi.org/10.1214/09-aihp311
Publication status	Published - Feb 2010

Keywords

strong law of large numbers
fragmentation processes
additive martingales

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10.1214/09-aihp311

Harris_AIHP-PS_2010_46_1_119.pdf

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title = "Strong law of large numbers for fragmentation processes",

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 eta for 1 > eta > 0.",

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AU - Knobloch, Robert

AU - Kyprianou, Andreas E

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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

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UR - http://dx.doi.org/10.1214/09-aihp311

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DO - 10.1214/09-aihp311

M3 - Article

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JO - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

IS - 1

ER -

Strong law of large numbers for fragmentation processes

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Keywords

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