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Semi-selfdecomposable distributions and a new class of limit theorems
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  • Published: September 1998

Semi-selfdecomposable distributions and a new class of limit theorems

  • Makoto Maejima1 &
  • Yoshihiro Naito1 

Probability Theory and Related Fields volume 112, pages 13–31 (1998)Cite this article

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  • 24 Citations

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Abstract.

Self-decomposable distributions are given as limits of normalized sums of independent random variables. We define semi-selfdecomposable distributions as limits of subsequences of normalized sums. More generally, we introduce a way of making a new class of limiting distributions derived from a class of distributions by taking the limits through subsequences of normalized sums, and define the class of semi-selfdecomposable distributions and a decreasing sequence of subclasses of it. We give two kinds of necessary and sufficient conditions for distributions belonging to those classes, one is in terms of the decomposability of random variables and another is in terms of Lévy measures.

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Authors and Affiliations

  1. Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223, Japan e-mail: maejima@math.keio.ac.jp, , , , , , JP

    Makoto Maejima & Yoshihiro Naito

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  1. Makoto Maejima
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  2. Yoshihiro Naito
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Received: 1 May 1997 / Revised version: 5 February 1998

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Maejima, M., Naito, Y. Semi-selfdecomposable distributions and a new class of limit theorems. Probab Theory Relat Fields 112, 13–31 (1998). https://doi.org/10.1007/s004400050181

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  • Issue Date: September 1998

  • DOI: https://doi.org/10.1007/s004400050181

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  • Mathematics Subject Classification (1991): 60E07 (primary); 60E10
  • 60F05
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