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Asymptotics of Maxima of Strongly Dependent Gaussian Processes

Part of: Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Zhongquan Tan ,
Enkelejd Hashorva  and
Zuoxiang Peng
Zhongquan Tan*
Affiliation:
Soochow University
Enkelejd Hashorva*
Affiliation:
University of Lausanne
Zuoxiang Peng*
Affiliation:
Southwest University
*
∗ Current address: College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, P. R. China.
∗∗ Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: enkelejd.hashorva@unil.ch
∗∗∗ Postal address: School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China.
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Abstract

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Let {Xn(t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|Xn(t)| is established as rn(t), the correlation function of {Xn(t), t∈[0,∞)}, n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

Keywords

Stationary Gaussian processstrong dependenceBerman's conditionlimit theoremPickands' constant

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 4 , December 2012 , pp. 1106 - 1118
Copyright
© Applied Probability Trust 

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