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December 2012 Asymptotics of maxima of strongly dependent Gaussian processes
Zhongquan Tan, Enkelejd Hashorva, Zuoxiang Peng
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J. Appl. Probab. 49(4): 1106-1118 (December 2012). DOI: 10.1239/jap/1354716660

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).

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Zhongquan Tan. Enkelejd Hashorva. Zuoxiang Peng. "Asymptotics of maxima of strongly dependent Gaussian processes." J. Appl. Probab. 49 (4) 1106 - 1118, December 2012. https://doi.org/10.1239/jap/1354716660

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1259.60039
MathSciNet: MR3058991
Digital Object Identifier: 10.1239/jap/1354716660

Subjects:
Primary: 60G15
Secondary: 60G70

Keywords: Berman's condition , limit theorem , Pickands' constant , stationary Gaussian process , Strong dependence

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 4 • December 2012
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