Weighted sums for i. i. d. random variables with relatively thin tails
type: Item
instance of: scholarly article
title: Weighted sums for i. i. d. random variables with relatively thin tails
zbMATH Open document ID: 0956.60013
DOI: 10.2307/3318632
author: H. Lanzinger
author: Ulrich Stadtmüller
published in: Bernoulli
publication date: 2001-03-07T00:00:00Z
review text: Strong limit theorems are proved for a sequence of weighted sums \(T_n= \sum^\infty_{k=1} a_{nk}X_k\) \((n= 1,2,\dots)\), where \((a_{nk})_{n,k= 1,2,\dots}\) is a double array satisfying \(\sum^\infty_{k=1} a_{nk}< \infty\) for each \(n\), and where \((X_k)_{k= 1,2,\dots}\) is an i.i.d. sequence with \(EX_1= 0\), and \(E\exp(t|X_1|)^{1/p})< \infty\) in a neighbourhood of \(t= 0\), for some \(p>0\). For special choices of weights, necessity of moment conditions can also be obtained. Various strong laws, based on summability methods, and their convergence rates are discussed including Cesàro, Euler and random walk methods as well as Valiron and running means. The results complement earlier work of Lanzinger (1995, 1998) and Li et al. (1995).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1428370
zbMATH Keywords: weighted sums of i.i.d. random variables
zbMATH Keywords: thin tails
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: Baum-Katz law
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/3318632
OpenAlex ID: W2010102105
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description: scientific article; zbMATH DE number 1428370