Central limit asymptotics for shifts of finite type
type: Item
instance of: scholarly article
title: Central limit asymptotics for shifts of finite type
zbMATH Open document ID: 0701.60026
DOI: 10.1007/BF02937307
author: Zaqueu Coelho
author: William Parry
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The authors prove the Berry-Esséen bound in the central limit theorem for Hölder-continuous functions on a shift of finite type endowed with a Gibbs measure [cf. \textit{Y. Guivarc'h} and \textit{J. Hardy}, Ann. Inst. Henri Poincaré, Probab. Stat. 24, 73-98 (1988; Zbl 0649.60041)]. Moreover, if f has a non lattice distribution the asymptotic expansion up to order o(1/\(\sqrt{n})\) is determined, and under certain moment conditions higher order approximations are derived. The method of proof is based on the theory of Perron-Frobenius operators [cf. \textit{J. Rousseau-Egele}, Ann. Probab. 11, 772-788 (1983; Zbl 0518.60033)].
reviewed by: Manfred Denker
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 4149258
zbMATH Keywords: Berry-Esséen bound
zbMATH Keywords: central limit theorem
zbMATH Keywords: Perron-Frobenius operators
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02937307
OpenAlex ID: W1978273259
description: scientific article; zbMATH DE number 4149258