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On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields

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Abstract

The partial-sum processes, indexed by sets, of a stationary nonuniform φ-mixing random field on the d-dimensional integer lattice are considered. A moment inequality is given from which the convergence of the finite-dimensional distributions to a Brownian motion on the Borel subsets of [0, 1]d is obtained. A Uniform CLT is proved for classes of sets with a metric entropy restriction and applied to certain Gibbs fields. This extends some results of Chen(5) for rectangles. In this case and when the variables are bounded a simpler proof of the uniform CLT is given.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Casilla De Correo 172, 1900, La Plata, Argentina

    Alberto L. Maltz

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  1. Alberto L. Maltz
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Maltz, A.L. On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields. Journal of Theoretical Probability 12, 643–660 (1999). https://doi.org/10.1023/A:1021619613916

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  • DOI: https://doi.org/10.1023/A:1021619613916

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