Almost sure and complete convergence of randomly weighted sums of independent random elements in Banach spaces
type: Item
instance of: scholarly article
title: Almost sure and complete convergence of randomly weighted sums of independent random elements in Banach spaces
zbMATH Open document ID: 1246.60046
author: Le Van Thanh
author: G. Yin
published in: Taiwanese Journal of Mathematics
publication date: 2011-12-01T00:00:00Z
review text: This work develops almost sure and complete convergence of randomly weighted sums of independent random elements in a real separable Banach space. Sufficient conditions for almost sure convergence and complete convergence in the sense defined by \textit{P. L. Hsu} and \textit{H. Robbins} [Proc. Natl. Acad. Sci. USA 33, 25--31 (1947; Zbl 0030.20101)] and \textit{P. Erdős} [Ann. Math. Stat. 20, 286-291 (1949; Zbl 0033.29001)] are provided. Examples showing that the conditions cannot he removed or weakened are given. It is also demonstrated that some of the known theorems in the literature [\textit{D. Li}, \textit{M. B. Rao}, \textit{T. Jiang} and \textit{X. Wang}, J. Theor. Probab. 8, No. 1, 49--76 (1995; Zbl 0814.60026); \textit{X. Wang}, \textit{M. B. Rao} and \textit{X. Yang}, Stochastic Anal. Appl. 11, No. 1, 115--132 (1993; Zbl 0764.60037)] are special cases of the result, published in this paper.
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 5984261
zbMATH Keywords: almost sure convergence
zbMATH Keywords: complete convergence
zbMATH Keywords: random weight
zbMATH Keywords: row-wise independent
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406378
OpenAlex ID: W1937615185
DOI: 10.11650/TWJM/1500406378
description: scientific article; zbMATH DE number 5984261