Extremes of order statistics of stationary processes

Krzysztof Dȩbicki, Enkelejd Hashorva, Lanpeng Ji, Chengxiu Ling*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Let (Formula presented.) be independent copies of a stationary process (Formula presented.). For given positive constants u,T, define the set of rth conjunctions (Formula presented.) with (Formula presented.) the rth largest order statistics of (Formula presented.). In numerous applications such as brain mapping and digital communication systems, of interest is the approximation of the probability that the set of conjunctions (Formula presented.) is not empty. Imposing the Albin’s conditions on X, in this paper we obtain an exact asymptotic expansion of this probability as u tends to infinity. Furthermore, we establish the tail asymptotics of the supremum of the order statistics processes of skew-Gaussian processes and a Gumbel limit theorem for the minimum order statistics of stationary Gaussian processes.

Original languageEnglish
Pages (from-to)229-248
Number of pages20
Issue number2
Publication statusPublished - 26 Jun 2015
Externally publishedYes


  • Albin’s conditions
  • Conjunction
  • Generalized Albin constant
  • Gumbel limit theorem
  • Order statistics process
  • Skew-Gaussian process

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