Invariance principles for sums of extreme sequential order statistics attracted to L evy processes Arnold
نویسنده
چکیده
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 L evy process. In addition, we get an approximation of these L evy processes by a nite number of extremal processes. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 60F17; 60G50
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