The accuracy of Gaussian approximations in nilpotent Lie groups
type: Item
instance of: scholarly article
title: The accuracy of Gaussian approximations in nilpotent Lie groups
zbMATH Open document ID: 0884.60008
DOI: 10.1007/BF02214261
author: Vidmantas Bentkus
author: Gyula Pap
published in: Journal of Theoretical Probability
publication date: 1998-03-19T00:00:00Z
review text: The paper contains refinements of a central limit theorem of \textit{A. Raugi} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 43, 149--172 (1978; Zbl 0394.60009)] on a class of stratified nilpotent Lie groups. The authors note that ``the only result known on nilpotent Lie groups is a Berry-Esseen type bound for probabilities of homogeneous balls due to \textit{G. Pap} [J. Multivariate Anal. 38, No. 2, 333--365 (1991; Zbl 0746.60011)]. This bound is obtained under relatively stringent moment assumptions whereas the assumptions in this paper seem to be optimal''.
reviewed by: Audrey A. Terras
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 1018709
zbMATH Keywords: central limit theorem
zbMATH Keywords: stratified nilpotent Lie groups
zbMATH Keywords: Edgeworth expansions
MaRDI profile type: Publication
Wikidata QID: Q115392708
cites work: Q4289671
cites work: Q4164574
cites work: Q5620554
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups
cites work: The domains of partial attraction of probabilities on groups and on vector spaces
cites work: Sharp pointwise estimate for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups
cites work: Q4153376
cites work: Limit theorems for probability measures on simply connected nilpotent Lie groups
cites work: Rate of convergence in CLT on stratified groups
cites work: Q4840478
cites work: Q4838528
cites work: Uniqueness of embedding into a Gaussian semigroup on a nilpotent Lie group
cites work: Rates of convergence of \(\alpha\)-stable random motions
cites work: Th�or�me de la limite centrale sur les groupes nilpotents
cites work: Croissance et mouvements browniens d'un groupe de Lie nilpotent et simplement connexe
cites work: Q4855436
cites work: Fourier analysis and limit theorems for convolution semigroups on a locally compact group
cites work: Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group
cites work: Contractive automorphisms on locally compact groups
cites work: Q3742109
cites work: Limit Theorems for Compositions of Distributions on Certain Nilpotent Lie Groups
full work available at URL: https://doi.org/10.1007/bf02214261
OpenAlex ID: W1983928632
description: scientific article; zbMATH DE number 1018709