Invariance principles for sums of extreme sequential order statistics attracted to Lévy processes
type: Item
instance of: scholarly article
title: Invariance principles for sums of extreme sequential order statistics attracted to Lévy processes
zbMATH Open document ID: 0997.60031
DOI: 10.1016/S0304-4149(99)00078-2
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: Let \(X_{n,i}\), \(1\leq i \leq n\), be a rowwise i.i.d. triangular array of random variables and let \(X_{i:[nt]}^{(n)}\) denote the \(i\)th smallest sequential order statistic of \(X_{n,1}, \dots , X_{n,[nt]}, \;0\leq t \leq 1.\) Strong convergence results and the invariance principle for centered partial sums of the first \(k\) sequential order statistics \(X_{i:[nt]}^{(n)}\) attracted to an infinitely divisible law are established. The quantile approach based on a representation of order statistics of i.i.d. uniformly distributed random variables is used to prove the joint strong convergence of sequential order statistics to extremal processes.
reviewed by: Zuzana Prášková
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 1792503
zbMATH Keywords: extremal processes
zbMATH Keywords: Lévy process
zbMATH Keywords: infinitely divisible law
zbMATH Keywords: sequential order statistics
zbMATH Keywords: invariance principle
author: Arnold Janssen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1792503