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A Subclass of Type G Selfdecomposable Distributions on ℝ d

Author

Listed:
  • Takahiro Aoyama

    (Keio University)

  • Makoto Maejima

    (Keio University)

  • Jan Rosiński

    (University of Tennessee)

Abstract

A new class of type G selfdecomposable distributions on ℝ d is introduced and characterized in terms of stochastic integrals with respect to Lévy processes. This class is a strict subclass of the class of type G and selfdecomposable distributions, and in dimension one, it is strictly bigger than the class of variance mixtures of normal distributions by selfdecomposable distributions. The relation to several other known classes of infinitely divisible distributions is established.

Suggested Citation

  • Takahiro Aoyama & Makoto Maejima & Jan Rosiński, 2008. "A Subclass of Type G Selfdecomposable Distributions on ℝ d," Journal of Theoretical Probability, Springer, vol. 21(1), pages 14-34, March.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0129-3
    DOI: 10.1007/s10959-007-0129-3
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    Cited by:

    1. Ken-iti Sato, 2013. "Inversions of Infinitely Divisible Distributions and Conjugates of Stochastic Integral Mappings," Journal of Theoretical Probability, Springer, vol. 26(4), pages 901-931, December.

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