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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

On a measure theoretical dynamical system with spectral gap property weconsider non-integrable observables with regularly varying tails and fulfillinga mild mixing condition. We show that the normed trimmed sum process of theseobservables then converges in mean. This result is new also for the specialcase of i.i.d. random variables and contrasts the general case where meanconvergence might fail even though a strong law of large numbers holds. Toilluminate the required mixing condition we give an explicit example of adynamical system fulfilling a spectral gap property and an observable withregularly varying tails but without the assumed mixing condition such that meanconvergence fails.

Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails