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

In this paper, we consider projection estimates for L\'evy densities inhigh-frequency setup. We give a unified treatment for different sets of basisfunctions and focus on the asymptotic properties of the maximal deviationdistribution for these estimates. Our results are based on the idea toreformulate the problems in terms of Gaussian processes of some special typeand to further analyze these Gaussian processes. In particular, we construct asequence of excursion sets, which guarantees the convergence of the deviationdistribution to the Gumbel distribution. We show that the rates of convergencepresented in previous articles on this topic are logarithmic and construct thesequences of accompanying laws, which approximate the deviation distributionwith polynomial rate.

Convergence rates of maximal deviation distribution for projection estimates of L\'evy densities