Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms)
type: Item
instance of: scholarly article
title: Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms)
zbMATH Open document ID: 0731.60025
DOI: 10.1007/BF01903836
author: Rainer Wittmann
published in: Acta Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: The author shows for i.i.d. random variables \(X_ i\) with a symmetric distribution function F that \[ (*)\;\limsup | X_ n| /(\max_{1\leq i\leq n-1}| S_ i|)=\infty \] if and only if \(EX^ 2_ 1=\infty\). In the other extreme case of positive random variables, an old result of Kesten states the equivalence of (*) with the non- existence of the first moment.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 4209206
zbMATH Keywords: random walk
zbMATH Keywords: maximal terms
zbMATH Keywords: non-existence of the first moment
reviewed by: Herold Dehling
MaRDI profile type: Publication
cites work: Q4183968
cites work: The Influence of the Maximum Term in the Addition of Independent Random Variables
cites work: The Strong Law of Large Numbers When the Mean is Undefined
cites work: Q5667812
cites work: The Limit Points of a Normalized Random Walk
description: scientific article; zbMATH DE number 4209206