A functional law of the iterated logarithm for associated sequences
type: Item
instance of: scholarly article
title: A functional law of the iterated logarithm for associated sequences
zbMATH Open document ID: 0578.60032
DOI: 10.1016/0167-7152(85)90020-3
author: Andre R. Dabrowski
published in: Statistics \& Probability Letters
publication date: 1985-01-01T00:00:00Z
review text: Recently a functional central limit theorem has been demonstrated for classes of associated random variables in a paper of \textit{C. M. Newman} and \textit{A. L. Wright}, Ann. Probab. 9, 671-675 (1981; Zbl 0465.60009). This paper provides certain useful inequalities on the joint characteristic function of normalized partial sums of associated random variables. The results of \textit{I. Berkes} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 26, 246-258 (1973; Zbl 0246.60020)] yield a functional law of the iterated logarithm for sequences of dependent random variables satisfying a condition on joint characteristic functions. These two results, and some calculations, are combined in the current paper to establish a functional law of the iterated logarithm for associated sequences. The rate at which the variance of the properly normalized partial sums approaches its limit is assumed to be polynomial.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 3925888
zbMATH Keywords: functional central limit theorem
zbMATH Keywords: functional law of the iterated logarithm
MaRDI profile type: Publication
full work available at URL: 0167-7152(85)90020-3
OpenAlex ID: W2025666984
cites work: The functional law of the iterated logarithm for dependent random variables
cites work: Q3843987
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cites work: An invariance principle for the law of the iterated logarithm
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description: scientific article; zbMATH DE number 3925888