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Extreme values and the law of the iterated logarithm
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  • Published: September 1987

Extreme values and the law of the iterated logarithm

  • J. Kuelbs1 &
  • M. Ledoux2 

Probability Theory and Related Fields volume 74, pages 319–340 (1987)Cite this article

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  • 15 Citations

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Summary

IfX takes values in a Banach spaceB and is in the domain of attraction of a Gaussian law onB, thenX satisfies the compact law of the iterated logarithm (LIL) with respect to a regular normalizing sequence {γ n } iffX satisfies a certain integrability condition. The integrability condition is equivalent to the fact that the maximal term of the sample {‖X 1‖, ‖X 2‖,..., ‖X n‖} does not dominate the partial sums {S n}, and here we examine the precise influence of these maximal terms and its relation to the compactLIL. In particular, it is shown that if one deletes enough of the maximal terms there is always a compactLIL with non-trivial limit set.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    J. Kuelbs

  2. Département de Mathématique, Université de Strasbourg, F-67084, Strasbourg, France

    M. Ledoux

Authors
  1. J. Kuelbs
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  2. M. Ledoux
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Additional information

Supported in part by NSF Grant MCS-8219742

Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742

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Kuelbs, J., Ledoux, M. Extreme values and the law of the iterated logarithm. Probab. Th. Rel. Fields 74, 319–340 (1987). https://doi.org/10.1007/BF00699094

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  • Received: 23 September 1984

  • Revised: 01 March 1986

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF00699094

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Keywords

  • Central Limit Theorem
  • Integrability Condition
  • Iterate Logarithm
  • Finite Dimensional Subspace
  • Maximal Term
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