Which i.i.d. sums are recurrently dominated by their maximal terms?
type: Item
instance of: scholarly article
title: Which i.i.d. sums are recurrently dominated by their maximal terms?
zbMATH Open document ID: 0777.60066
DOI: 10.1007/BF01047571
author: Rainer Wittmann
author: Michael J. Klass
published in: Journal of Theoretical Probability
publication date: 1993-12-15T00:00:00Z
review text: Let \((X_ n)_{n\geq 1}\) be i.i.d. random variables with common distribution function \(F\) and \(P(X_ 1\neq 0)>0\). Put \(S_ n=\sum^ n_{i=1} X_ i\), \(S^*_ 0=0\), \(S^*_ n=\sup_{1\leq i\leq n}| S_ i|\), \(n\geq 1\). The authors characterize \(\limsup_{n\to\infty} (X_ n/S^*_{n-1})=\infty\) a.s. in terms of the distribution function \(F\). It turns out that their results are generalizations of previous results by \textit{H. Kesten} [Ann. Math. Stat. 41, 1173-1205 (1970; Zbl 0233.60062)] and \textit{R. Wittmann} [Acta Math. Hung. 56, No. 3/4, 225-228 (1990; Zbl 0731.60025)].
reviewed by: S.Grigorescu
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G70
zbMATH DE Number: 179061
zbMATH Keywords: random walks
zbMATH Keywords: symmetric random walks
MaRDI profile type: Publication
cites work: Q4183968
cites work: The Strong Law of Large Numbers When the Mean is Undefined
cites work: The Limit Points of a Normalized Random Walk
cites work: The growth of random walks and Levy processes
cites work: Summen unabhängiger Zufallsvariablen, die durch die Maximalterme dominiert werden. (Sums of independent random variables which are dominated by maximal terms)
description: scientific article; zbMATH DE number 179061