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Central limit asymptotics for shifts of finite type

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Abstract

We study the rate of convergence and asymptotic expansions in the central limit theorem for the class of Hölder continuous functions on a shift of finite type endowed with a stationary equilibrium state. It is shown that the rate of convergence in the theorem isO(n −1/2) and when the function defines a non-lattice distribution an asymptotic expansion to the order ofo(n −1/2) is given. Higher-order expansions can be obtained for a subclass of functions. We also make a remark on the central limit theorem for (closed) orbital measures.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK

    Zaqueu Coelho & William Parry

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  1. Zaqueu Coelho
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  2. William Parry
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Dedicated to Horst Michel and his family

Financially supported by FAPESP and on leave from: Instituto de Matemática e Estatística, Universidade de São Paulo, Brasil.

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Coelho, Z., Parry, W. Central limit asymptotics for shifts of finite type. Israel J. Math. 69, 235–249 (1990). https://doi.org/10.1007/BF02937307

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  • DOI: https://doi.org/10.1007/BF02937307

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