A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution
type: Item
instance of: scholarly article
title: A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution
zbMATH Open document ID: 0641.60036
DOI: 10.1016/0304-4149(87)90037-8
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: The main result is: partial sums of i.i.d. r.v. when suitably normed and centred \((S_ n-a_ n)/B_ n\) are in the domain of partial attraction of the normal distribution iff the set of almost sure limit points of the random polygon as a sequence in C[0,1] or of the partial sum process \((S_{[nt]}-a_{[nt]})/B_ n\) as a sequence in D[0,1], equals to the unit ball of absolutely continuous functions in \(L_ 2\) metric. It is proved that the same statement holds true after removing a fixed number of terms of largest modulus from \(S_ n\).
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4044853
zbMATH Keywords: functional law of iterated logarithm
zbMATH Keywords: trimmed variables
zbMATH Keywords: domain of partial attraction
author: Ross A. Maller
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90037-8
OpenAlex ID: W2006835384
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description: scientific article; zbMATH DE number 4044853