Skip to main content
SpringerLink
Log in

A characterization of the convolution of Gaussian and Poisson distributions

  • Published:
Sankhya A Aims and scope Submit manuscript

Abstract

A characterization of the convolution of Gaussian and Poisson laws in the set of infinitely divisible distributions is provided.

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

  • Csörgő, S. (2005). A probabilistic proof of Kruglov’s theorem on the tails of infinitely divisible distributions. Acta Sci. Math., 71, 405–415.

    Google Scholar 

  • Kruglov, V.M. (1970). A note on the theory of infinitely divisible laws. Theory Probab. Appl., 15, 319–324.

    Article  MathSciNet  Google Scholar 

  • Kruglov, V.M. (1972). Integrals with respect to infinitely divisible distributions in a Hilbert space. Math. Notes, 11, 407–411.

    Article  MathSciNet  MATH  Google Scholar 

  • Kruglov, V.M. (2003). Normal and Poisson convergence. Theory Probab. Appl., 48, 392–398.

    MathSciNet  Google Scholar 

  • Kruglov, V.M. (2010). A characterization of the Poisson distribution. Statist. Probab. Lett., 80, 2032–2034.

    Article  MathSciNet  MATH  Google Scholar 

  • Kruglov, V.M. and Antonov, C.N. (1982). On asymptotic behaviour of infinitely divisible distributions in Banach space. Theory Probab. Appl., 27, 667–687.

    Article  MathSciNet  MATH  Google Scholar 

  • Loève, M. (1977). Probability theory, I (4th ed.). Springer-Verlag, New York.

    Book  MATH  Google Scholar 

  • Rossberg, H.-J., Jesiak, B. and Siegel, G. (1985). Analytical methods of probability theory. Akademie-Verlag, Berlin.

    Google Scholar 

  • Sato, K.-I. (1999). Levy processes and infinitely divisible distributions. University Press, Cambridge.

    MATH  Google Scholar 

  • Yakymiv, A.L. (2005). Probabilistic applications of Tauberian theorems. VSP, Leiden-Boston.

    Book  MATH  Google Scholar 

Download references

Acknowledgement

Research supported by the Russian Foundation for Basic Research, projects 11-01-00515-a.

The author is indebted to an anonymous referee for helpful comments that lead to a better presentation of the results.

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Vorobyovy Gory, 119992, GSP-1, Moscow, Russia

    Victor M. Kruglov

Authors
  1. Victor M. Kruglov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Victor M. Kruglov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kruglov, V.M. A characterization of the convolution of Gaussian and Poisson distributions. Sankhya A 74, 1–9 (2012). https://doi.org/10.1007/s13171-012-0005-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13171-012-0005-9

AMS (2000) subject classification

Keywords and phrases

Search

Navigation