An example on the central limit theorem for associated sequences
type: Item
instance of: scholarly article
title: An example on the central limit theorem for associated sequences
zbMATH Open document ID: 0544.60033
author: Norbert Herrndorf
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: \textit{C. M. Newman} [Commun. Math. Phys. 74, 119-128 (1980; Zbl 0429.60096)] and \textit{C. M. Newman} and \textit{A. L. Wright} [Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009)] conjectured that the central limit theorem holds for strictly stationary associated sequences \((X_ n)\) with \(K(R)=Var(X_ 1)+2\sum^{R}_{j=2}Cov(X_ 1,X_ j)\) slowly varying as \(R\to \infty\). The content of this paper is a counterexample to this conjecture.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3866281
zbMATH Keywords: central limit theorem
zbMATH Keywords: stationary associated sequences
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993241
OpenAlex ID: W2022409209
DOI: 10.1214/AOP/1176993241
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description: scientific article; zbMATH DE number 3866281