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Russian Mathematical Surveys, 2013, Volume 68, Issue 4, Pages 721–761
DOI: https://doi.org/10.1070/RM2013v068n04ABEH004851 (Mi rm9537) 		 
This article is cited in 13 scientific papers (total in 13 papers)

The accuracy of strong Gaussian approximation for sums of independent random vectors

A. Yu. Zaitsevab

a St. Petersburg State University
b St. Petersburg Department of V. A. Steklov Institute of the Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (903 kB) Citations (13) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2013v068n04ABEH004851
Abstract: This paper is a survey of recent results on the accuracy of strong Gaussian approximation for sums of independent random vectors. They give multidimensional generalizations of one-dimensional results due to Komlós, Major, and Tusnády, as well as to Sakhanenko, and improve upon Einmahl's multidimensional results. Infinite-dimensional analogues of these results are also presented.
Bibliography: 102 titles.
Keywords: multidimensional invariance principle, strong approximation, sums of independent random vectors.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00256
Ministry of Education and Science of the Russian Federation НШ-1216.2012.01
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 09.04.2013
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: 60F17
Language: English
Original paper language: Russian
Citation: A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721–761
Citation in format AMSBIB
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\paper The accuracy of strong Gaussian approximation for sums of independent random vectors
\jour Russian Math. Surveys
\yr 2013
\vol 68
\issue 4
\pages 721--761
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  • https://doi.org/10.1070/RM2013v068n04ABEH004851
  • https://www.mathnet.ru/eng/rm/v68/i4/p129
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:771
    Russian version PDF:416
    English version PDF:85
    References:50
    First page:14
     
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