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Free Infinitely Divisible Approximations of n-Fold Free Convolutions

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Prokhorov and Contemporary Probability Theory

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

Abstract

Based on the method of subordinating functions we prove a free analog of error bounds in classical Probability Theory for the approximation of n-fold convolutions of probability measures by infinitely divisible distributions.

Mathematics Subject Classification (2010): 46L53, 46L54, 60E07

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Acknowledgements

This research was supported by CRC 701, Bielefeld University.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Gennadii Chistyakov & Friedrich Götze

  2. Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine

    Gennadii Chistyakov

Authors
  1. Gennadii Chistyakov
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  2. Friedrich Götze
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Corresponding author

Correspondence to Gennadii Chistyakov .

Editor information

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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Chistyakov, G., Götze, F. (2013). Free Infinitely Divisible Approximations of n-Fold Free Convolutions. 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_12

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