Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces
type: Item
instance of: scholarly article
title: Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces
zbMATH Open document ID: 0806.60002
DOI: 10.1007/BF01874465
author: Ferenc Móricz
author: Kuo-Liang Su
author: Robert L. Taylor
published in: Acta Mathematica Hungarica
publication date: 1994-09-13T00:00:00Z
review text: This paper contains a discussion of conditions under which \({1 \over m^ \alpha n^ \beta} \sum^ m_{i = 1} \sum^ n_{j = 1} X_{ij} \to 0\) a.s., where \(\{X_{ij}\}\) is an array of orthogonal Banach space- valued random elements with suitable moment conditions. The concept of orthogonality used here is the James type. One of the major results shows that strong laws of large numbers may be obtained even in the case of real-valued random variables under weaker conditions than those usually given, the moment conditions allowing for \(p\)-th moments, \(1 \leq p \leq 2\), rather than the more usual 2nd order moments.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 638236
zbMATH Keywords: James orthogonality
zbMATH Keywords: orthogonal Banach space-valued random elements
zbMATH Keywords: strong laws of large numbers
reviewed by: Andrew Dale
MaRDI profile type: Publication
cites work: Strong limit theorems for quasi-orthogonal random fields
cites work: Moment inequalities and the strong laws of large numbers
cites work: SLLN and Convergence Rates for Nearly Orthogonal Sequences of Random Variables
cites work: Strong Laws of Large Numbers for Arrays of Orthogonal Random Variables
cites work: Stochastic convergence of weighted sums of random elements in linear spaces
full work available at URL: https://doi.org/10.1007/bf01874465
OpenAlex ID: W2002549433
description: scientific article; zbMATH DE number 638236