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

Let $\{Z(\tau,s), (\tau,s)\in [a,b]\times[0,T]\}$ with some positiveconstants $a,b,T$ be a centered Gaussian random field with variance function$\sigma^{2}(\tau,s)$ satisfying $\sigma^{2}(\tau,s)=\sigma^{2}(\tau)$. Wefirstly derive the exact tail asymptotics for the maximum$M_{H}(T)=\max_{(\tau,s)\in[a,b]\times[0,T]}Z(\tau,s)/\sigma(\tau)$ up crossingsome level $u$ with any fixed $0<a<b<\infty$ and $T>0$; and we further derivethe extreme limit law for $M_{H}(T)$. As applications of the main results, wederive the exact tail asymptotics and the extreme limit law for Sheppstatistics with stationary Gaussian process, fractional Brownian motion andGaussian integrated process as input.

Extremes of a type of locally stationary Gaussian random fields with applications to Shepp statistics