On Chung-Teicher type strong law for arrays of vector-valued random variables
type: Item
instance of: scholarly article
title: On Chung-Teicher type strong law for arrays of vector-valued random variables
zbMATH Open document ID: 1072.60021
DOI: 10.1155/S0161171204301031
author: Anna Kuczmaszewska
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51695
review text: Sufficient conditions for the strong law of large numbers (SLLN) on a separable Banach space \(B\) are usually given under the geometric assumption that \(B\) is of Rademacher type \(p\) for some \(1<p\leq2\). The author considers arrays \(\{X_{ni}:\,1\leq i\leq k_n,\,n\geq1\}\) of rowwise independent \(B\)-valued random variables and studies the equivalence of a weak law of large numbers (WLLN) to its strong version \(\sum_{i=1}^{k_n}a_{ni}X_{ni}\to0\) almost surely, for some weights \(a_{ni}\in\mathbb R\setminus\{0\}\). The presented sufficient conditions for equivalence of WLLN and SLLN are of Chung type or Chung-Teicher type. Although the results are formulated for general separable Banach spaces \(B\), the assumptions made have some relationship to the Rademacher type \(p\) condition. Consequently, sufficient conditions for SLLN on Rademacher type \(p\) spaces are derived. For the Chung-Teicher type SLLN an essential simplification is made when assuming the random variables to be stochastically dominated and the weights to build a Toeplitz array.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 2168624
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: rowwise independent array
zbMATH Keywords: separable Banach space
zbMATH Keywords: Rademacher type \(p\)
zbMATH Keywords: Chung type
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2168624