Clustering behavior of finite variance partial sum processes
type: Item
instance of: scholarly article
title: Clustering behavior of finite variance partial sum processes
zbMATH Open document ID: 0832.60037
DOI: 10.1007/BF01198849
author: Uwe Einmahl
author: Victor W. Goodman
publication date: 1996-02-13T00:00:00Z
review text: The authors obtain clustering rates in Strassen's functional law of the iterated logarithm for finite variance partial sum processes in one dimension. They also obtain a general characterization of these rates which enables them in matching the rates of Brownian motion for a partial sum process at points \(f\) inside the Strassen set \(K\) and also at points on the boundary of \(K\). Somewhat surprisingly the results are obtained under relatively mild moment conditions on a partial sum process. The proof is based on a strong approximation result that is particularly efficient for large excursions of normalized partial sum processes.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 800494
zbMATH Keywords: clustering rates
zbMATH Keywords: Strassen's functional law of the iterated logarithm
zbMATH Keywords: Brownian motion
zbMATH Keywords: strong approximation result
zbMATH Keywords: large excursions
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 800494