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Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments

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The aim of this paper is to derive consequences of a result of Götze and Zaitsev (2008). We show that the i.i.d. case of this result implies a multidimensional version of some results of Sakhanenko (1985). We establish bounds for the rate of strong Gaussian approximation of sums of i.i.d. R d-valued random vectors ξ j having finite moments E IIξ j IIγ, γ>2. Bibliography: 13 titles.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany

    F. Götze

  2. St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia

    A. Yu. Zaitsev

Authors
  1. F. Götze
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  2. A. Yu. Zaitsev
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Correspondence to F. Götze.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 110–121.

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Götze, F., Zaitsev, A.Y. Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments. J Math Sci 167, 495–500 (2010). https://doi.org/10.1007/s10958-010-9935-8

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  • DOI: https://doi.org/10.1007/s10958-010-9935-8

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