Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions
type: Item
instance of: scholarly article
title: Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions
zbMATH Open document ID: 0646.60008
DOI: 10.1016/0047-259X(88)90054-1
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The authors provide a proof of the SLLN in separable Banach spaces in the general framework of pairwise independent random elements and consider almost sure convergence to 0, as \(n\to \infty\), of weighted sums, \(\sum_{k\geq 1}a_{nk}X_ k\), of random elements in a separable Banach space, where \(\{a_{nk}\); n,k\(\geq 1\}\) is a Toeplitz sequence of real numbers. The basic results in the paper are proved by using an extension due to Blackwell and Dubins of the Skorokhod representation theorem applied to weakly equivalent sequences of probability measures.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4054678
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: Toeplitz sequence of real numbers
zbMATH Keywords: Skorokhod representation theorem
zbMATH Keywords: weakly equivalent sequences of probability measures
author: Juan Antonio Cuesta
author: Carlos Matrán
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4054678