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Uniform Integrability and the Central Limit Theorem for Strongly Mixing Processes

  • Manfred Denker
  • C. M. Goldie
  • G. J. Morrow
Part of the Progress in Probability and Statistics book series (PRPR, volume 11)

Abstract

It is shown that for a strongly mixing sequence the central limit theorem holds if and only if the squares of the normalised partial sums are uniformly integrable.

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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Manfred Denker
    • 1
  • C. M. Goldie
    • 2
  • G. J. Morrow
    • 3
  1. 1.Institut für Mathematische StochastikGeorg-August-UniversitätGöttingenWest Germany
  2. 2.Mathematics DivisionUniversity of SussexBrightonEngland
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA

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