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Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions
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  • Published: 17 July 2007

Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions

  • Ph. Barbe1 &
  • W. P. McCormick2 

Probability Theory and Related Fields volume 141, pages 155–180 (2008)Cite this article

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Abstract

We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results.

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Author information

Authors and Affiliations

  1. CNRS, 90 rue de Vaugirard, 75006, Paris, France

    Ph. Barbe

  2. Department of Statistics, University of Georgia, Athens, GA, 30602, USA

    W. P. McCormick

Authors
  1. Ph. Barbe
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  2. W. P. McCormick
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Correspondence to W. P. McCormick.

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Barbe, P., McCormick, W.P. Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions. Probab. Theory Relat. Fields 141, 155–180 (2008). https://doi.org/10.1007/s00440-007-0082-1

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  • Received: 22 January 2006

  • Revised: 16 May 2007

  • Published: 17 July 2007

  • Issue Date: May 2008

  • DOI: https://doi.org/10.1007/s00440-007-0082-1

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Keywords

  • Asymptotic expansion
  • Convolution
  • Tail area approximation
  • Regular variation
  • Subexponential distributions
  • Infinite order moving average
  • Weighted sum of random variables

Mathematics Subject Classifications (2000)

  • Primary: 60F99
  • 60G50
  • Secondary: 62E20
  • 62M10
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