Stochastic summability methods for domains of normal attraction of semistable laws
type: Item
instance of: scholarly article
title: Stochastic summability methods for domains of normal attraction of semistable laws
zbMATH Open document ID: 1076.60018
DOI: 10.1023/B:JOTH.0000027026.21519.45
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-28T00:00:00Z
review text: Semistable laws arise as limit distributions of affine normalized sums or maxima of i.i.d.\ random variables along a subsequence \((k_n)\) with geometrical growth \(k_{n+1}/k_n\to c>1\). While in general the distributions do not converge along the entire sequence \(k_n=n\), for the special case of sampling sequences with \(k_n/c^n\to1\) it is shown that limitation can be achieved with certain stochastic summability methods. The summability methods can be interpreted as taking independent random samples \(T_n\to\infty\) in probability, whose mantissa for base \(c\), i.e.\ \(\mathcal M_c(T_n)=T_n/c^{\lfloor\log_cT_n\rfloor}\in[1,c)\), converges in distribution. Some examples of such summability methods are also given. Among these are logarithmic summation and certain modifications in which cases the limiting distribution is a logarithmic mixture of semistable laws.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 11K99
zbMATH DE Number: 2183270
zbMATH Keywords: semistable distribution
zbMATH Keywords: domain of attraction
zbMATH Keywords: stochastic summability
zbMATH Keywords: mantissa distribution
zbMATH Keywords: random summation
author: Peter Kern
MaRDI profile type: Publication
full work available at URL: b:joth.0000027026.21519.45
OpenAlex ID: W2066112123
description: scientific article; zbMATH DE number 2183270