A nonuniform bound on the rate of convergence in the martingale central limit theorem
type: Item
instance of: scholarly article
title: A nonuniform bound on the rate of convergence in the martingale central limit theorem
zbMATH Open document ID: 0656.60034
author: Erich Haeusler
author: Konrad Joos
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: The main result of the paper is a sharp nonuniform bound of the rate of convergence in the central limit theorem for martingale differences having finite moments of order 2-2\(\delta\) for some \(0<\delta <\infty\). The method of the proof is the ``nonuniform'' modification of the first author's version of the iterative method developed by Bolthausen [Ann. Probab. 16, No.1, 275-299 (1988; Zbl 0639.60030)]. A nonuniform bound for the rate of convergence of discrete-time martingales to mixtures of normal distributions is obtained as a consequence of the main result.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4072027
zbMATH Keywords: mixtures of normal distributions
zbMATH Keywords: rate of convergence in the central limit
zbMATH Keywords: rate of convergence of discrete-time martingales
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991592
OpenAlex ID: W1975517094
DOI: 10.1214/AOP/1176991592
description: scientific article; zbMATH DE number 4072027