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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let {ξj}j∈Z be a sequence of random variables which belong to the domain of attraction of a linear fractional stable motion {∆H,α(t)} with infinite variance. We study the convergence of weighted sums In(f) := An ∑ j∈Z f(j/n)ξj with a suitable scaling An, to I(f) := ∫∞ −∞ f(u)d∆H,α(u) in distribution under suitable assumptions on a class of deterministic functions f . We also show that if {ft, t ≥ 0} are the kernel functions from the “moving average” representation of a linear fractional stable motion with another index H ′, then {In(ft)} converges to a linear fractional stable motion {∆H+H′−1/α,α(t)}.

Limit Theorems for Weighted Sums of Infinite Variance Random Variables Attracted to Integrals of Linear Fractional Stable Motions