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Asymptotic distribution for the sum and maximum of Gaussian processes

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

W. P. McCormick  and
Y. Qi
W. P. McCormick*
Affiliation:
University of Georgia
Y. Qi*
Affiliation:
University of Georgia
*
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602-1952, USA.
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602-1952, USA.
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Abstract

Previous work on the joint asymptotic distribution of the sum and maxima of Gaussian processes is extended here. In particular, it is shown that for a stationary sequence of standard normal random variables with correlation function r, the condition r(n)ln n = o(1) as n → ∞ suffices to establish the asymptotic independence of the sum and maximum.

Keywords

Gaussian processmaximumsumweakly dependentstrongly dependent

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60G15: Gaussian processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 958 - 971
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

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