Skip to main content
SpringerLink
Log in

A Subclass of Type G Selfdecomposable Distributions on ℝd

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

A new class of type G selfdecomposable distributions on ℝd 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aoyama, T., Maejima, M.: Characterizations of subclasses of type G distributions on ℝd by stochastic integral representations. Bernoulli 13, 148–160 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Barndorff-Nielsen, O.E., Maejima, M., Sato, K.: Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations. Bernoulli 12, 1–33 (2006)

    MATH  MathSciNet  Google Scholar 

  3. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II, 2nd edn. Wiley, New York (1966)

    MATH  Google Scholar 

  4. Jurek, Z.J.: Relations between the s–selfdecomposable and selfdecomposable measures. Ann. Probab. 13, 592–608 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Maejima, M., Rosiński, J.: The class of type G distributions on ℝd and related subclasses of infinitely divisible distributions. Demonstr. Math. 34, 251–266 (2001)

    MATH  Google Scholar 

  6. Maejima, M., Rosiński, J.: Type G distributions on ℝd. J. Theor. Probab. 15, 323–341 (2002)

    Article  MATH  Google Scholar 

  7. Rosinski, J.: On a class of infinitely divisible processes represented as mixture of Gaussian processes. In: Cambanis, S., et al. (eds.) Stable Processes and Related Topics, pp. 27–41. Birkhäuser, Basel (1991)

    Google Scholar 

  8. Sato, K.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  9. Sato, K.: Additive processes and stochastic integrals. Ill. J. Math. 50(Doob volume), 825–851 (2006)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Takahiro Aoyama & Makoto Maejima

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1300, USA

    Jan Rosiński

Authors
  1. Takahiro Aoyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Makoto Maejima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Rosiński
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takahiro Aoyama.

Additional information

Research of J. Rosiński supported, in part, by a grant from the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aoyama, T., Maejima, M. & Rosiński, J. A Subclass of Type G Selfdecomposable Distributions on ℝd . J Theor Probab 21, 14–34 (2008). https://doi.org/10.1007/s10959-007-0129-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10959-007-0129-3

Keywords

Mathematics Subject Classification (2000)

Search

Navigation