A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups
type: Item
instance of: scholarly article
title: A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups
zbMATH Open document ID: 0926.60019
DOI: 10.1007/BF02362290
published in: Journal of Mathematical Sciences (New York)
publication date: 1998-11-24T00:00:00Z
review text: This paper is concerned with an iterated logarithm type result for the normed sum of a geometrically increasing number of i.i.d. random vectors \(\{X_i,i=1,2, \dots\}\) in \(d\)-dimensional Euclidean space which have an infinitely divisible law without Gaussian component. It is shown that the result also applies in the case of corresponding distributions on certain homogeneous groups, in particular Heisenberg groups. It is also shown that in the case \(d=1\) the results hold if the \(X_i\) just belong to the domain of normal attraction of the relevant infinitely divisible law. The primary result is new even in the one-dimensional case.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1213226
zbMATH Keywords: iterated logarithm law
zbMATH Keywords: semistable laws
zbMATH Keywords: homogeneous groups
author: Hans-Peter Scheffler
MaRDI profile type: Publication
cites work: A Law of the Iterated Logarithm for Stable Summands
cites work: Q5545069
cites work: Q3339837
cites work: Harmonic Analysis in Phase Space. (AM-122)
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Q3327409
cites work: Q3331981
cites work: Q4734550
cites work: A smooth subadditive homogeneous norm on a homogeneous group
cites work: On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law
cites work: Semi-stable probability measures on $R^{N}$
cites work: On the Extension of the Class of Stable Distributions
cites work: \({\mathcal D}\)-domains of attraction of stable measures on stratified Lie groups
cites work: Q4838530
cites work: Domains of semi-stable attraction of nonnormal semi-stable laws
cites work: Q3704678
cites work: A law of the iterated logarithm for distributions in the generalized domain of attraction of a nondegenerate Gaussian law
full work available at URL: https://doi.org/10.1007/bf02362290
OpenAlex ID: W1983631003
description: scientific article; zbMATH DE number 1213226