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A law of the iterated logarithm for distributions in the generalized domain of attraction of a nondegenerate Gaussian law
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  • Published: June 1986

A law of the iterated logarithm for distributions in the generalized domain of attraction of a nondegenerate Gaussian law

  • Daniel Charles Weiner1 

Probability Theory and Related Fields volume 72, pages 337–357 (1986)Cite this article

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Summary

When operators T n exist such that for sums S n of n i.i.d. copies of a finite-dimensional random vector X we have T n S n is shift-convergent in distribution to a standard Gaussian law, a necessary and sufficient condition on the distribution of X is given for the appropriate law of the iterated logarithm using the operators T n to hold. Our result extends certain well-known real line L.I.L.'s; it utilizes a necessary and sufficient condition due to Hahn and Klass for T n to exist giving a Gaussian limit law, and employs a second moment technique due to Kuelbs and Zinn.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Nebraska, 68588-0323, Lincoln, NE, USA

    Daniel Charles Weiner

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  1. Daniel Charles Weiner
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Charles Weiner, D. A law of the iterated logarithm for distributions in the generalized domain of attraction of a nondegenerate Gaussian law. Probab. Th. Rel. Fields 72, 337–357 (1986). https://doi.org/10.1007/BF00334190

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  • Received: 21 October 1984

  • Revised: 20 October 1985

  • Issue Date: June 1986

  • DOI: https://doi.org/10.1007/BF00334190

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Random Vector
  • Real Line
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