On the smallest maximal increment of partial sums of i.i.d. random variables
type: Item
instance of: scholarly article
title: On the smallest maximal increment of partial sums of i.i.d. random variables
zbMATH Open document ID: 0878.60026
author: Uwe Einmahl
author: David M. Mason
publication date: 1997-12-14T00:00:00Z
review text: The authors study the almost sure limiting behaviour of the minimum \(m_n(k_n)\) of maximal increments of partial sums (suitably centered and normalized), taken over subintervals of size \(k_n\) in a large interval of size \(n\). The limiting behaviour is different for the cases (i) \(k_n/\log n\to\infty\), (ii) \(k_n=O(\log n)\), or (iii) \(k_n=o(\log n)\) as \(n\to\infty\). Lim inf and lim sup results are obtained under almost no assumptions on the underlying distribution. Relations to an earlier result of Csörgö and Révész (1981) are also discussed.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 1014206
zbMATH Keywords: smallest maximal increment of partial sums
zbMATH Keywords: strong limit theorem
zbMATH Keywords: Feller class
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
full work available at URL: s004400050101
OpenAlex ID: W2072681041
DOI: 10.1007/S004400050101
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1014206