Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables
type: Item
instance of: scholarly article
title: Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables
zbMATH Open document ID: 1253.60046
DOI: 10.1155/2012/104390
author: Qunying Wu
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far, no general moment inequality for PNQD sequences has been given, and therefore the study of the limit theory for PNQD sequences is very difficult and challenging. We establish a collection that contains a relationship to overcome the difficulty that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by \textit{L. E. Baum} and \textit{M. Katz} [Trans. Am. Math. Soc. 120, 108--123 (1965; Zbl 0142.14802)] and \textit{Q. Wu} and \textit{Y. Wang} [J. Syst. Sci. Math. Sci. 22, No. 2, 192--199 (2002; Zbl 1038.60020)].
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 6106111
zbMATH Keywords: pairwise negative quadrant dependent random variables
zbMATH Keywords: limit theory
zbMATH Keywords: general moment inequality
zbMATH Keywords: complete convergence
Wikidata QID: Q58905699
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/104390
OpenAlex ID: W2091690245
cites work: Some Concepts of Dependence
cites work: A note on the almost sure convergence of sums of negatively dependent random variables
cites work: Strong convergence of pairwise NQD random sequences
cites work: The strong law of large numbers for pairwise NQD random variables
cites work: Q4528312
cites work: Q4778490
cites work: An application of Stein's method to limit theorems for pairwise negative quadrant dependent random variables
cites work: Convergence rates for probabilities of moderate deviations for moving average processes
cites work: On the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm
cites work: Convergence Rates in the Law of Large Numbers
cites work: The strong law of large numbers for \(B\)-valued random fields
description: scientific article; zbMATH DE number 6106111