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Asymptotic distribution of sum and maximum for Gaussian processes

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Hwai-Chung Ho  and
William P. McCormick
Hwai-Chung Ho*
Affiliation:
Academia Sinica
William P. McCormick*
Affiliation:
University of Georgia
*
∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, ROC.
∗∗Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA. Email address: [email protected].
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Abstract

Let {Xn, n ≥ 0} be a stationary Gaussian sequence of standard normal random variables with covariance function r(n) = EX0Xn. Let Under some mild regularity conditions on r(n) and the condition that r(n)lnn = o(1) or (r(n)lnn)−1 = O(1), the asymptotic distribution of is obtained. Continuous-time results are also presented as well as a tube formula tail area approximation to the joint distribution of the sum and maximum.

Keywords

Gaussian processmaximumsumstrongly dependent

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F05: Central limit and other weak theorems 60G15: Gaussian processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1031 - 1044
Copyright
Copyright © Applied Probability Trust 1999 

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