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June, 1974 Limit Theorems for the Maximum Term of a Stationary Process
G. L. O'Brien
Ann. Probab. 2(3): 540-545 (June, 1974). DOI: 10.1214/aop/1176996673

Abstract

This paper contains necessary and sufficient conditions, which sometimes coincide, for the limiting distribution of a uniformly (or strongly) mixing stationary process to be the same as for the independent process with the same marginal distributions. Examples with different limits are given. Let $H$ be any distribution function and let $c_n(\xi) = \inf \{x \in R: H(x) \geqq 1 - \xi/n\}$. The limiting behavior of $H^n(c_n(\xi))$ is determined.

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G. L. O'Brien. "Limit Theorems for the Maximum Term of a Stationary Process." Ann. Probab. 2 (3) 540 - 545, June, 1974. https://doi.org/10.1214/aop/1176996673

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.60018
MathSciNet: MR362450
Digital Object Identifier: 10.1214/aop/1176996673

Subjects:
Primary: 60F05
Secondary: 60G10

Keywords: independent process , limit distributions , maximum value , stationary process , uniform or strong mixing

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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