Journal of Applied Probability

Asymptotics of maxima of strongly dependent Gaussian processes

Zhongquan Tan, Enkelejd Hashorva, and Zuoxiang Peng

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Abstract

Let {Xn(t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of \supt∈[0,T(n)]|X n(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).

Article information

Source
J. Appl. Probab., Volume 49, Number 4 (2012), 1106-1118.

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1354716660

Digital Object Identifier
doi:10.1239/jap/1354716660

Mathematical Reviews number (MathSciNet)
MR3058991

Zentralblatt MATH identifier
1259.60039

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes

Keywords
Stationary Gaussian process strong dependence Berman's condition limit theorem Pickands' constant

Citation

Tan, Zhongquan; Hashorva, Enkelejd; Peng, Zuoxiang. Asymptotics of maxima of strongly dependent Gaussian processes. J. Appl. Probab. 49 (2012), no. 4, 1106--1118. doi:10.1239/jap/1354716660. https://projecteuclid.org/euclid.jap/1354716660


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