Invariance principles for sums of extreme sequential order statistics attracted to Levy processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:85

Article

Janssen, A

关键词: extremal process;    Levy process;    infinitely divisible law;    sequential order statistics;    almost sure convergence in the Skorohod space;    Poissonian representation;    invariance principle;   

DOI  :  10.1016/S0304-4149(99)00078-2

来源: Elsevier

【 摘 要 】

The paper establishes strong convergence results for the joint convergence of sequential order statistics. There exists an explicit construction such that almost sure convergence to extremal processes follows. If a partial sum of rowwise i.i.d. random variables is attracted by a non-Gaussian limit law then the results apply to invariance principles for sums of extreme sequential order statistics which turn out to be almost surely convergent or convergent in probability in D[0, 1]. Under certain conditions they converge to the non-Gaussian part of the Levy process. In addition, we get an approximation of these Levy processes by a finite number of extremal processes. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free