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On One Inequality for Characteristic Functions

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Prokhorov and Contemporary Probability Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 33))

Abstract

This paper deals with an inequality for characteristic functions. This inequality (see (3) below) founds connection between “measure of almost normality” and characteristic functions. Also an analysis of accuracy in the local limit theorem and connection between the central limit and local limit theorem are given.

Mathematics Subject Classification (2010): 60E10, 60E15

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References

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

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  2. Gamkrelidze, N.G.: On a lower estimation of the rate of convergence in the local limit theorem. Litovski mat. sb. 7(3), 405–408 (1968) (In Russian)

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  3. Gamkrelidze, N.G.: On the connection between the local and the integral theorem for lattice distributions. Theory Probab. Appl. 131, 174–179 (1968)

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  4. Gnedenko, B.V., Kolmogorov, A.N.: Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading (1954)

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  5. Petrov, V.V.: Sums of Independent Random Variables. Springer, Berlin (1975)

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Acknowledgements

This note would not have been written without the support of acad. Yu. Prokhorov. To him go my foremost thanks.

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Authors and Affiliations

  1. Gubkin Russian State University of Oil and Gas, Leninsky Prospekt, 65, 119991, Moscow, Russia

    Nicko Gamkrelidze

Authors
  1. Nicko Gamkrelidze
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Correspondence to Nicko Gamkrelidze .

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Editors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow, 119991, Russia

    Albert N. Shiryaev

  2. Courant Institute, New York University, Mercer Street 252, New York, 10012, New York, USA

    S. R. S. Varadhan

  3. Central Economics & Math. Institute, Russian Academy of Sciences, Nakhimovsky Pr. 47, Moscow, 117418, Russia

    Ernst L. Presman

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Gamkrelidze, N. (2013). On One Inequality for Characteristic Functions. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_15

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