On complete convergence for weighted sums of arrays of dependent random variables
type: Item
instance of: scholarly article
title: On complete convergence for weighted sums of arrays of dependent random variables
zbMATH Open document ID: 1231.60025
DOI: 10.1155/2011/630583
author: Soo Hak Sung
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: Summary: The rate of complete convergence for weighted sums of arrays of row-wise independent random variables was obtained by \textit{S. H. Sung} and \textit{A. Volodin} [Stochastic Anal. Appl. 29, No.~2, 282--291 (2011; Zbl 1217.60007)]. In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences of \(\varphi\)-mixing and \(\rho^\ast\)-mixing random variables are also obtained. Our results improve and generalize the results of \textit{J.-I. Baek, M.-H. Ko} and \textit{T.-S. Kim} [J. Korean Math. Soc. 45, No.~4, 1101--1111 (2008; Zbl 1148.60012)], \textit{A. Kuczmaszewska} [Stat. Probab. Lett. 79, No.~1, 116--124 (2009; Zbl 1154.60319)] and \textit{X. Wang} et al. [J. Inequal. Appl. 2010, Article~ID 372390 (2010; Zbl 1208.60031)].
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 5997813
zbMATH Keywords: complete convergence
zbMATH Keywords: negatively associated and negatively dependent random variables
zbMATH Keywords: \(\varphi\)-mixing and \(\rho^\ast\)-mixing random variables
Wikidata QID: Q58654360
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/630583
OpenAlex ID: W1982465117
cites work: Complete Convergence and the Law of Large Numbers
cites work: On a Theorem of Hsu and Robbins
cites work: On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes
cites work: On the complete convergence of weighted sums for arrays of negatively associated variables
cites work: A Note on the Rate of Complete Convergence for Weighted Sums of Arrays of Banach Space Valued Random Elements
cites work: On complete convergence for arrays of rowwise negatively associated random variables
cites work: On complete convergence for weighted sums of \(\varphi \)-mixing random variables
cites work: Complete convergence for weighted sums of random variables
cites work: Q3924997
cites work: Negative association of random variables, with applications
cites work: A comparison theorem on moment inequalities between negatively associated and independent random variables
cites work: Some Concepts of Dependence
cites work: Rosenthal's type inequalities for negatively orthant dependent random variables
cites work: Maximal inequalities and an invariance principle for a class of weakly dependent random variables
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description: scientific article; zbMATH DE number 5997813