Approximation of distributions of integral additive functions by discrete charges. I
type: Item
instance of: scholarly article
title: Approximation of distributions of integral additive functions by discrete charges. I
zbMATH Open document ID: 0683.10041
DOI: 10.1007/BF00972224
author: Jonas Šiaulys
author: Vydas Čekanavičius
published in: Lithuanian Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: The paper has nothing to do with the stated approximation of the title. Rather, it estimates three different metrics between probability distributions or charges, with emphasis on the distributions being products of a large number of discrete distributions (charges). The term `charge' means a signed measure which may take as value either plus or minus infinity (but not both). The convergence of these metrics to zero implies weak convergence, so the estimates can be used for proving limit theorems. It is mentioned that, in a subsequent paper (see the following review Zbl 0683.10042), the approximation stated in the title will be given by utilizing the inequalities of the present paper.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 4118463
zbMATH Keywords: Fourier transform
zbMATH Keywords: factorial moments
zbMATH Keywords: metrics between probability distributions
zbMATH Keywords: charges
zbMATH Keywords: discrete distributions
zbMATH Keywords: signed measure
zbMATH Keywords: limit theorems
reviewed by: Janos Galambos
MaRDI profile type: Publication
cites work: Q3807318
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full work available at URL: https://doi.org/10.1007/bf00972224
OpenAlex ID: W4256589183
description: scientific article; zbMATH DE number 4118463