Estimates for the rapid decay of concentration functions of \(n\)-fold convolutions
type: Item
instance of: scholarly article
title: Estimates for the rapid decay of concentration functions of \(n\)-fold convolutions
zbMATH Open document ID: 0936.60014
DOI: 10.1023/A:1022654631571
published in: Journal of Theoretical Probability
publication date: 2000-05-09T00:00:00Z
review text: For a probability distribution \(F\) defined on the Bord \(\sigma\)-field of subsets of the real line \(R\), its concentration function is defined as \(Q(F,b) =\sup_xF\{[x,x+b]\}\) for any \(b\geq 0\). Let \(F^n\) be the \(n\)-fold convolution of \(F\). This paper deals with the classical question on the rate of decay of \(Q(F^n,b)\) as \(n\to\infty\). Some upper bounds are presented for \(Q(F^n, b)\) based on the estimates in the central limit theorem and some elementary properties of concentration functions. These results are refinements of some earlier results obtained by other authors and their proofs are also different from most of the previous papers, where the method of characteristic functions had been used extensively.
reviewed by: Dongsheng Tu
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1208779
zbMATH Keywords: concentration function
zbMATH Keywords: rate of decay
zbMATH Keywords: convolutions
zbMATH Keywords: central limit theorem
author: Friedrich Götze
author: A. Yu. Zaitsev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1208779