Strong laws of large numbers for weighted sums of random elements in normed linear spaces
type: Item
instance of: scholarly article
title: Strong laws of large numbers for weighted sums of random elements in normed linear spaces
zbMATH Open document ID: 0679.60009
DOI: 10.1155/S0161171289000657
author: Andrew Rosalsky
author: André Adler
author: Robert L. Taylor
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46402
review text: Let \(\{V_ n,n\geq 1\}\) be a sequence of independent random elements in a real separable normed linear space and let \(\{a_ n\}\), \(\{b_ n\}\) be sequences of constants with \(0<b_ n\uparrow \infty\). The main results discussed here provide conditions under which \(\{a_ n(V_ n-E V_ n)\), \(n>1\}\) obeys a strong law of large numbers of the form \[ \sum^{n}_{j=1}a_ j(V_ j-E V_ j)/b_ n\to 0\quad a.s. \] It is further shown that Feller's generalization of the Marcinkiewicz-Zygmund SLLN holds for random elements in a real separable Rademacher type p \((1<p\leq 2)\) Banach space.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 4113627
zbMATH Keywords: almost sure convergence
zbMATH Keywords: normed weighted sums
zbMATH Keywords: random elements in a real separable normed linear space
zbMATH Keywords: strong law of large numbers
reviewed by: Andrew Dale
MaRDI profile type: Publication
OpenAlex ID: W2106435985
description: scientific article; zbMATH DE number 4113627