The strong law of large numbers for weighted averages under dependence assumptions
type: Item
instance of: scholarly article
title: The strong law of large numbers for weighted averages under dependence assumptions
zbMATH Open document ID: 0857.60021
DOI: 10.1007/BF02214087
published in: Journal of Theoretical Probability
publication date: 1997-03-03T00:00:00Z
review text: The authors prove strong laws of large numbers for weighted averages of dependent random variables, generalizing the classical work of \textit{B. Jamison}, \textit{S. Orey} and \textit{W. Pruitt} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 4, 40-44 (1965; Zbl 0141.16404)] for i.i.d. sequences. The dependence structure imposed is asymptotic quadrant sub-independent, requiring that \[ P(X_i>s, X_j>t) - P(X_i>s) P(X_j>t) \leq q \bigl(|i-j |\bigr) \alpha_{ij} (s,t), \] together with a similar condition on \(P(X_i<s, X_j<t)\). This condition generalizes the notion of asymptotic quadrant independence, introduced by \textit{T. Birkel} [Stat. Probab. Lett. 7, No. 1, 17-20 (1988; Zbl 0661.60048)]. The authors also prove a Marcinkiewicz-Zygmund SLLN for weighted averages. The proofs make heavy use of unpublished results by the same authors.
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 934239
zbMATH Keywords: law of large numbers
zbMATH Keywords: summability methods
zbMATH Keywords: weak dependence
author: Tapas K. Chandra
author: Subhashis Ghosal
reviewed by: Herold Dehling
MaRDI profile type: Publication
cites work: Laws of large numbers under dependence assumptions
cites work: Q3980511
cites work: Q4251585
cites work: Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables
cites work: Stability of sums of weighted nonnegative random variables
cites work: Q3911791
cites work: Convergence of weighted averages of independent random variables
cites work: A maximal inequality and dependent strong laws
cites work: Q5541672
cites work: Q5609799
cites work: Q3766573
description: scientific article; zbMATH DE number 934239