Skip to main content
Log in

Lower and upper bounds for characteristic functions

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In the paper, several known inequalities for characteristic functions are sharpened and several new ones are derived.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. L. Doob,Stochastic Processes, Wiley, Chapman and Hall, New York (1953).

    Google Scholar 

  2. V. V. Petrov,Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  3. Yu. V. Prokhorov and Yu. A. Rozanov,Probability Theory [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  4. V. A. Statulevichus, “Limit theorems for densities and asymptotic decompositions for distributions of sums of independent random variables,”Teor. Veroyatn Primen.,10, No. 4, 645–659 (1965).

    Google Scholar 

  5. N. G. Ushakov, “Some inequalities for the characteristic functions of unimodal distributions,”Teor. Veroyatn. Primen.,26, No. 3, 606–609 (1981).

    MATH  MathSciNet  Google Scholar 

  6. N. G. Ushakov, “Upper estimations of the maximal probability for sums of independent random vectors,”Teor. Veroyatn. Primen.,30, No. 1, 33–43 (1985).

    MATH  MathSciNet  Google Scholar 

  7. R. Yanushkevichius,Stability for Characterizations of Distributions [in Russian], Mokslas, Vilnius (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ushakov, N.G. Lower and upper bounds for characteristic functions. J Math Sci 84, 1179–1189 (1997). https://doi.org/10.1007/BF02398431

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02398431

Keywords

Navigation