Extreme values and the law of the iterated logarithm
type: Item
instance of: scholarly article
title: Extreme values and the law of the iterated logarithm
zbMATH Open document ID: 0586.60009
DOI: 10.1007/BF00699094
author: Michel Ledoux
author: Jim Kuelbs
publication date: 1987-01-01T00:00:00Z
review text: If X takes values in a Banach space B and is in the domain of attraction of a Gaussian law on B, then X satisfies the compact law of the iterated logarithm (LIL) with respect to a regular normalizing sequence \(\{\gamma_ n\}\) iff X satisfies a certain integrability condition. The integrability condition is equivalent to the fact that the maximal term of the sample \(\{\| X_ 1\|,\| X_ 2\|,...,\| X_ n\| \}\) does not dominate the partial sums \(\{S_ n\}\), and here we examine the precise influence of these maximal terms and its relation to the compact LIL. In particular, it is shown that if one deletes enough of the maximal terms there is always a compact LIL with non-trivial limit set.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 3940294
zbMATH Keywords: cluster set
zbMATH Keywords: domain of attraction of a Gaussian random variable
zbMATH Keywords: extreme values
zbMATH Keywords: law of the iterated logarithm
MaRDI profile type: Publication
cites work: Exponential moments of vector valued random series and triangular arrays
cites work: Inequalities for B-valued random vectors with applications to the strong law of large numbers
cites work: A new proof of the Hartman-Wintner law of the iterated logarithm
cites work: Convergence of moments and related functional in the general central limit theorem in banach spaces
cites work: Some results on the cluster set \(C(\{S_n/a_n\})\) and the LIL
cites work: Q5538132
cites work: Q5667812
cites work: Some results on the LIL in Banach space with applications to weighted empirical processes
cites work: Relation entre th�or�me central-limite et loi du logarithme it�r� dans les espaces de Banach
cites work: Sums of independent Banach space valued random variables
cites work: A strong convergence theorem for Banach space valued random variables
cites work: Some results on LIL behavior
cites work: The LIL when X is in the domain of attraction of a Gaussian law
cites work: The strong law of large numbers when extreme terms are excluded from sums
cites work: Stability for sums of i.i.d. random variables when extreme terms are excluded
cites work: Q4188490
cites work: Q4084474
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3940294