On the strong law of large numbers for sums of pairwise independent random variables
type: Item
instance of: scholarly article
title: On the strong law of large numbers for sums of pairwise independent random variables
zbMATH Open document ID: 0842.60026
DOI: 10.1016/0167-7152(94)00201-I
published in: Statistics \& Probability Letters
publication date: 1996-03-11T00:00:00Z
review text: Consider a sequence \(X_1, X_2, \dots\) of pairwise independent and identically distributed random variables. Let \(S_0= 0\), \(S_n= X_1+ \dots+ X_n\) \((n\geq 1)\) denote their corresponding partial sums. The author proves the following (improved) version of a strong law of large numbers: If \(E|X_1 |^\gamma (\log^+ |X_1 |)^\tau< \infty\), where \(1< \gamma< 2\), \(\tau> 0\), and \(\tau> 4\gamma- 6\), then \((S_n- ES_n )/ n^{1/ \gamma}\to 0\) a.s. as \(n\to \infty\).
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 844715
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: almost sure convergence
zbMATH Keywords: pairwise independent random variables
author: A. I. Martikainen
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
cites work: A stationary pairwise independent absolutely regular sequence for which the central limit theorem fails
cites work: An elementary proof of the strong law of large numbers
cites work: Some pairwise independent sequences for which the central limit theorem fails
cites work: Q3810599
cites work: Q3843987
cites work: Q3362602
cites work: On a Theorem of Feller
cites work: Q4085017
cites work: Note on the Concept ofm-Dependence
cites work: Bemerkungen zum Gesetz der großen Zahlen
cites work: Bemerkung über paarweise unabhängige zufällige Größen. (Remark on pairwise independent random variables)
description: scientific article; zbMATH DE number 844715