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Dependence in Probability and Statistics pp 165–192Cite as

Birkhäuser

Basic Properties of Strong Mixing Conditions

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Part of the book series: Progress in Probability and Statistics ((PRPR,volume 11))

Abstract

This is a survey of the basic properties of strong mixing conditions for sequences of random variables. The focus will be on the “structural” properties of these conditions, and not at all on limit theory. For a discussion of central limit theorems and related results under these conditions, the reader is referred to Peligrad [60] or Iosifescu [50]. This survey will be divided into eight sections, as follows:

  1. 1.

    Measures of dependence

  2. 2.

    Five strong mixing conditions

  3. 3.

    Mixing conditions for two or more sequences

  4. 4.

    Mixing conditions for Markov chains

  5. 5.

    Mixing conditions for Gaussian sequences

  6. 6.

    Some other special examples

  7. 7.

    The behavior of the dependence coefficients

  8. 8.

    Approximation of mixing sequences by other random sequences.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, Indiana, 47405, USA

    Richard C. Bradley

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  1. Richard C. Bradley
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Editor information

Editors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Freiburg, 7800, Freiburg i. Br., Federal Republic of Germany

    Ernst Eberlein

  2. Department of Mathematics, Boston University, 02215, Boston, MA, USA

    Murad S. Taqqu

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Bradley, R.C. (1986). Basic Properties of Strong Mixing Conditions. In: Eberlein, E., Taqqu, M.S. (eds) Dependence in Probability and Statistics. Progress in Probability and Statistics, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8162-8_8

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  • DOI: https://doi.org/10.1007/978-1-4615-8162-8_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4615-8163-5

  • Online ISBN: 978-1-4615-8162-8

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