English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we prove a strong law of large numbers and its L^1-convergencecounterpart for the process counted with a random characteristic in the contextof self-similar fragmentation processes. This result extends a somewhatanalogical result by Nerman for general branching processes to fragmentationprocesses. In addition, we apply the general result of this paper to a specificexample that in particular extends a limit theorem, concerning thefragmentation energy, by Bertoin and Mart\'inez from L^1-convergence to almostsure convergence. Our approach treats fragmentation processes with an infinitedislocation measure directly, without using a discretisation method. Moreover,we obtain a result regarding the asymptotic behaviour of the empirical meanassociated with some stopped fragmentation process.

Asymptotic properties of the process counted with a random characteristic in the context of fragmentation processes