Limit theorems for sums of weakly dependent Banach space valued random variables

  • Herold Dehling


We prove an estimate for the Prohorov-distance in the central limit theorem for strong mixing Banach space valued random variables. Using a recent variant of an approximation theorem of Berkes and Philipp (1979) we obtain as a corollary a strong invariance principle for absolutely regular sequences with error term \(t^{\tfrac{1}{2} - \gamma }\). For strong mixing sequences we prove a strong invariance principle with error term o((t log logt)1/2).


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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Herold Dehling
    • 1
  1. 1.Institut für Mathematische Stochastik der UniversitätGöttingenFederal Republic of Germany

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