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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 368, Pages 110–121 (Mi znsl3506)  
This article is cited in 7 scientific papers (total in 7 papers)

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

F. Götzea, A. Yu. Zaitsevb

a Universität Bielefeld, Fakultät für Mathematik, Bielefeld, Germany
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (596 kB) Citations (7)
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Abstract: The aim of this paper is to derive consequences of a result of Götze and Zaitsev (2008). It is shown that in the case of i.i.d. summands 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 independent $\mathbf R^d$-valued random vectors $\xi_j$ having finite moments $\mathbf E\|\xi_j\|^\gamma$, $\gamma\ge2$. Bibl. – 13 titles.
Key words and phrases: multidimensional invariance principle, strong approximation, sums of independent random vectors.
Received: 20.11.2009
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 167, Issue 4, Pages 495–500
DOI: https://doi.org/10.1007/s10958-010-9935-8
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: F. Götze, A. Yu. Zaitsev, “Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments”, Probability and statistics. Part 15, Zap. Nauchn. Sem. POMI, 368, POMI, St. Petersburg, 2009, 110–121; J. Math. Sci. (N. Y.), 167:4 (2010), 495–500
Citation in format AMSBIB
\Bibitem{GotZai09}
\by F.~G\"otze, A.~Yu.~Zaitsev
\paper Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments
\inbook Probability and statistics. Part~15
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 368
\pages 110--121
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3506}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2749186}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 167
\issue 4
\pages 495--500
\crossref{https://doi.org/10.1007/s10958-010-9935-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953913762}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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