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Exact convergence rates for the bounded law of the iterated logarithm in Hilbert space
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  • Published: June 1992

Exact convergence rates for the bounded law of the iterated logarithm in Hilbert space

  • Uwe Einmahl1 

Probability Theory and Related Fields volume 92, pages 177–194 (1992)Cite this article

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Summary

In a previous paper we obtained upper and lower class type results refining the bounded LIL for sums of iid Hilbert space valued mean zero random variables, whose covariance operators satisfy certain regularity assumptions. We now establish precise convergence rates for the bounded LIL in the “non-regular” case. It turns out that the almost sure behavior in this case is entirely different from the behavior in the previous situation.

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Author information

Authors and Affiliations

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

    Uwe Einmahl

Authors
  1. Uwe Einmahl
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Additional information

Supported in part by NSF Grant DMS 90-05804

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Cite this article

Einmahl, U. Exact convergence rates for the bounded law of the iterated logarithm in Hilbert space. Probab. Th. Rel. Fields 92, 177–194 (1992). https://doi.org/10.1007/BF01194920

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  • Received: 28 January 1991

  • Revised: 14 October 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01194920

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Keywords

  • Covariance
  • Hilbert Space
  • Stochastic Process
  • Probability Theory
  • Convergence Rate
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