On the Gaussian approximation of convolutions under multidimensional analogues of S. N. Bernstein's inequality conditions
type: Item
instance of: scholarly article
title: On the Gaussian approximation of convolutions under multidimensional analogues of S. N. Bernstein's inequality conditions
zbMATH Open document ID: 0612.60031
DOI: 10.1007/BF00363515
publication date: 1987-01-01T00:00:00Z
review text: Let F be the distribution function of a sum of independent k-dimensional random vectors, and let \(\Phi\) be the Gaussian distribution with zero mean and the same covariance operator as F. The main results consider the closeness of F and \(\Phi\) ; in particular, an upper bound on the Lévy- Prohorov distance between F and \(\Phi\) is presented, and shown to be optimal, in the case of infinitely divisible distributions and certain distributions with exponentially-decreasing tails. The proofs are based on techniques used by \textit{V. V. Yurinskij} [Teor. Veroyatn. Primen. 22, 675-688 (1977; Zbl 0399.60022)]. Similar approximation results are given for density functions and conditional distributions.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 3990508
zbMATH Keywords: covariance operator
zbMATH Keywords: Lévy-Prohorov distance
zbMATH Keywords: infinitely divisible distributions
zbMATH Keywords: conditional distributions
author: A. Yu. Zaitsev
reviewed by: R. James Tomkins
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3990508