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Products of independent, normally attracted random variables
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  • Published: March 1988

Products of independent, normally attracted random variables

  • Peter Hall1 &
  • Eugene Seneta2 

Probability Theory and Related Fields volume 78, pages 135–142 (1988)Cite this article

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  • 1 Citations

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Summary

LetR n denote the correlation coefficient of ann-sample of pairs (X i ,Y i ), each distributed as (X, Y). AssumeX andY are independent and in the domain of attraction of the Normal law. It is shown that this entailsXY being in that domain of attraction, and thatd n R n →N(0, 1) in distribution for constantsd n satisfying lim sup(n 1/2/d n )≦1. Examples illustrate details of these limit theorems.

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References

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Authors and Affiliations

  1. Department of Statistics, Australian National University, G.P.O. Box 4, 2601, Canberra, ACT, Australia

    Peter Hall

  2. Department of Mathematical Statistics, University of Sydney, 2006, Sydney, N.S.W., Australia

    Eugene Seneta

Authors
  1. Peter Hall
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  2. Eugene Seneta
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Cite this article

Hall, P., Seneta, E. Products of independent, normally attracted random variables. Probab. Th. Rel. Fields 78, 135–142 (1988). https://doi.org/10.1007/BF00718041

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  • Received: 26 September 1986

  • Revised: 16 October 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718041

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Keywords

  • Stochastic Process
  • Probability Theory
  • Limit Theorem
  • Mathematical Biology
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