An analytic approach to the Markov chains recursive in the sense of Harris, and the Berry-Esseen estimate
type: Item
instance of: scholarly article
title: An analytic approach to the Markov chains recursive in the sense of Harris, and the Berry-Esseen estimate
zbMATH Open document ID: 0967.60072
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: In Theorem~1, a Berry-Esseen bound is given to describe the rate of convergence to normality of \(\frac 1{\sqrt{n}}\sum_{k=0}^ng(X_k)\) as \(n\to\infty\), where \(X_0,X_1,\ldots\) is a Markov chain conditioned on \(X_0=x\) and \(g\) is a measurable real function. The dependence of the bound on the moments and transition probabilities is made explicit. The result complements the bound given by \textit{E. Bolthausen} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 60, 283-289 (1982; Zbl 0476.60022)]. The relations between the norming quantities of Theorem~1 and those in preceding works are made explicit in Theorems~2 and 3.
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1557321
zbMATH Keywords: Markov chain
zbMATH Keywords: Berry-Esseen bound
zbMATH Keywords: asymptotic normality
author: Sergei Nagaev
reviewed by: M. P. Quine
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557321