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June, 1979 Maxima and Minima of Stationary Sequences
Richard A. Davis
Ann. Probab. 7(3): 453-460 (June, 1979). DOI: 10.1214/aop/1176995046

Abstract

We show that the asymptotic behavior of the normalized maxima of a stationary sequence satisfying a weak distributional mixing and bivariate condition is completely determined by the marginal distribution of the process. Sufficient conditions are given in order for the maxima and minima to be asymptotically independent. An example of a 1-dependent sequence where the maxima and minima are not asymptotically independent is also provided.

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Richard A. Davis. "Maxima and Minima of Stationary Sequences." Ann. Probab. 7 (3) 453 - 460, June, 1979. https://doi.org/10.1214/aop/1176995046

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60019
MathSciNet: MR528323
Digital Object Identifier: 10.1214/aop/1176995046

Subjects:
Primary: 60F05
Secondary: 60G10

Keywords: $m$-dependence , distributional mixing , maximum and minimum value , Nondegenerate limiting distributions , stationary Gaussian sequence , stationary sequence

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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