The Annals of Probability

Maxima and Minima of Stationary Sequences

Richard A. Davis

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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.

Article information

Source
Ann. Probab., Volume 7, Number 3 (1979), 453-460.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995046

Digital Object Identifier
doi:10.1214/aop/1176995046

Mathematical Reviews number (MathSciNet)
MR528323

Zentralblatt MATH identifier
0401.60019

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes

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

Citation

Davis, Richard A. Maxima and Minima of Stationary Sequences. Ann. Probab. 7 (1979), no. 3, 453--460. doi:10.1214/aop/1176995046. https://projecteuclid.org/euclid.aop/1176995046


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