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January, 1993 A Strong Invariance Principle Concerning the $J$-Upper Order Statistics for Stationary Gaussian Sequences
George Haiman, Madan L. Puri
Ann. Probab. 21(1): 86-135 (January, 1993). DOI: 10.1214/aop/1176989395

Abstract

It is shown that in the case of stationary Gaussian processes, the $J$th $(J \geq 1)$ record times $\{T_n, n \geq 1\}$ and the corresponding $J$-upper order statistics $\{X_{T_n - J + 1, T_n}, \ldots, X_{T_n, T_n}\}$ can almost surely be identified via a translation of the time index $n$ to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method for approximating sequences of record times and the corresponding upper order statistics introduced by Haiman (1987a, b) for the case $J = 1$ is extended and applied under weaker conditions concerning the covariance function, and also under different sets of new hypotheses.

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George Haiman. Madan L. Puri. "A Strong Invariance Principle Concerning the $J$-Upper Order Statistics for Stationary Gaussian Sequences." Ann. Probab. 21 (1) 86 - 135, January, 1993. https://doi.org/10.1214/aop/1176989395

Information

Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0772.60020
MathSciNet: MR1207217
Digital Object Identifier: 10.1214/aop/1176989395

Subjects:
Primary: 60F15
Secondary: 60G15 , 62G30

Keywords: Gaussian processes , order statistics , record times , Strong invariance

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 1 • January, 1993
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