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Extreme values and a Gaussian central limit theorem
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  • Published: September 1987

Extreme values and a Gaussian central limit theorem

  • J. Kuelbs1 &
  • M. Ledoux2 

Probability Theory and Related Fields volume 74, pages 341–355 (1987)Cite this article

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Summary

We examine the central limit theorem with Gaussian limit law for a sequence of independent, identically distributed, vector valued random variables whose partial sums can be centered and normalized to be tight with non-degenerate limit laws. These results apply to the situation when the sequence is in the domain of attraction of a non-degenerate stable law of indexp∈(0,2], and are achieved by eliminating the extreme values from the partial sums.

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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, 7, rue René Descartes, 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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Cite this article

Kuelbs, J., Ledoux, M. Extreme values and a Gaussian central limit theorem. Probab. Th. Rel. Fields 74, 341–355 (1987). https://doi.org/10.1007/BF00699095

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  • Received: 29 October 1984

  • Revised: 12 May 1986

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF00699095

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Keywords

  • Central Limit Theorem
  • Finite Dimensional Subspace
  • Local Limit Theorem
  • Gaussian Limit
  • Real Separable Banach Space
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