A note on the rate of convergence in the martingale central limit theorem
type: Item
instance of: scholarly article
title: A note on the rate of convergence in the martingale central limit theorem
zbMATH Open document ID: 0539.60023
author: Erich Haeusler
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: Applying the Skorokhod embedding scheme \textit{C. C. Heyde} and \textit{B. M. Brown} [Ann. Math. Stat. 41, 2161-2165 (1970; Zbl 0225.60026)] obtained an estimate of the rate of convergence in the central limit theorem for martingale differences with finite absolute moments of order \(2+2\delta\) for \(0<\delta \leq 1\). In the present note this estimate is extended to the range \(1<\delta<\infty\) (up to a logarithmic factor). The method of proof is a refinement of the classical Lindeberg-Lévy approach developed by \textit{E. Bolthausen}, Ann. Probab. 10, 672-688 (1982; Zbl 0494.60020).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 3858069
zbMATH Keywords: rate of convergence
zbMATH Keywords: central limit theorem for martingale differences
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993311
OpenAlex ID: W2045478662
DOI: 10.1214/AOP/1176993311
description: scientific article; zbMATH DE number 3858069