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The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions
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  • Published: 19 June 2008

The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

  • Makoto Maejima1 &
  • Ken-iti Sato2 

Probability Theory and Related Fields volume 145, pages 119–142 (2009)Cite this article

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Abstract

It is shown that the limits of the nested subclasses of five classes of infinitely divisible distributions on \({\mathbb{R}^{d}}\) , which are the Jurek class, the Goldie– Steutel–Bondesson class, the class of selfdecomposable distributions, the Thorin class and the class of generalized type G distributions, are identical with the closure of the class of stable distributions. More general results are also given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Makoto Maejima

  2. Hachiman-yama 1101-5-103, Tenpaku-ku, Nagoya, 468-0074, Japan

    Ken-iti Sato

Authors
  1. Makoto Maejima
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  2. Ken-iti Sato
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Correspondence to Makoto Maejima.

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Maejima, M., Sato, Ki. The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions. Probab. Theory Relat. Fields 145, 119–142 (2009). https://doi.org/10.1007/s00440-008-0163-9

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  • Received: 25 November 2007

  • Revised: 26 May 2008

  • Published: 19 June 2008

  • Issue Date: September 2009

  • DOI: https://doi.org/10.1007/s00440-008-0163-9

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Mathematics Subject Classification (2000)

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