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/

Zendy Plus

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

Zendy Tools

Zendy Open

This paper analyzes the limit properties of the empirical process of$\alpha$-stable random variables with long range dependence. The$\alpha$-stable random variables are constructed by non-linear transformationsof bivariate sequences of strongly dependent gaussian processes. The approachfollowed allows an analysis of the empirical process by means of expansions interms of bivariate Hermite polynomials for the full range $0<\alpha<2$. A weakuniform reduction principle is provided and it is shown that the limitingprocess is gaussian. The results of the paper different substantailly fromthose available for empirical processes obtained by stable moving averages withlong memory. An application to goodness-of-fit testing is discussed.

A note on the empirical process of strongly dependent stable random variables