Complete convergence of the maximum partial sums for arrays of rowwise of AANA random variables
type: Item
instance of: scholarly article
title: Complete convergence of the maximum partial sums for arrays of rowwise of AANA random variables
zbMATH Open document ID: 1269.60037
DOI: 10.1155/2013/741901
author: Aiting Shen
author: Yan Chen
author: Yu Zhou
author: Ranchao Wu
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: The limiting behavior of the maximal partial sums \[ (1/a_n)\max_{1 \leq j \leq n}| \sum^j_{i=1} X_{ni}| \] is investigated, and some new results are obtained, where \(\{x_{ni}, i \geq 1, n \geq 1\}\) is an array of row-wise AANA random variables and \(\{a_n, n \geq 1\}\) is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of row-wise AANA random variables is obtained. The results extend and improve the corresponding ones of \textit{T.-C. Hu} and \textit{R. L. Taylor} [Int. J. Math. Math. Sci. 20, No. 2, 375--382 (1997; Zbl 0883.60024)] for arrays of row-wise independent random variables.
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 6175115
zbMATH Keywords: arrays of row-wise of asymptotically almost negatively associated (AANA) random variables
zbMATH Keywords: limiting behavior
zbMATH Keywords: maximum partial sums
zbMATH Keywords: Chung-type strong law of large numbers
Wikidata QID: Q58921790
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/741901
OpenAlex ID: W2066428309
cites work: Q4040465
cites work: On Chung-Teicher type strong law of large numbers for \(\rho ^{\ast }\)-mixing random variables
cites work: On the strong law for arrays and for the bootstrap mean and variance
cites work: On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables
cites work: Negative association of random variables, with applications
cites work: A law of the iterated logarithm of partial sums for NA random variables
cites work: Chover's law of the iterated logarithm for negatively associated sequences
cites work: An almost sure central limit theorem for the weight function sequences of NA random variables
cites work: Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables
cites work: Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables
cites work: The strong law of large numbers for weighted averages under dependence assumptions
cites work: The strong law of large numbers and the law of the iterated logarithm for product sums of NA and AANA random variables
cites work: The Hájek-Rényi inequality for the AANA random variables and its applications
cites work: Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications
cites work: Convergence properties for asymptotically almost negatively associated sequence
cites work: MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES
cites work: Complete convergence for arrays of rowwise asymptotically almost negatively associated random variables
cites work: On complete convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables
cites work: Strong convergence properties for asymptotically almost negatively associated sequence
cites work: On complete convergence of moving average process for AANA sequence
Recommended article: On complete convergence for arrays of rowwise AANA random variables
Recommended article: Convergence Properties of the Maximal Partial Sums for Arrays of Rowwise NA Random Variables
Recommended article: Complete convergence and complete moment convergence for arrays of rowwise ANA random variables
Recommended article: A note on complete convergence of weighted sums for array of rowwise AANA random variables
Recommended article: Q5399082
Recommended article: Q5490435
Recommended article: Q5708934
Recommended article: Q3176098
Recommended article: On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables
Recommended article: On complete convergence for arrays of rowwise dependent random variables
description: scientific article; zbMATH DE number 6175115