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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 1, Pages 100–123
DOI: https://doi.org/10.4213/tvp2484 (Mi tvp2484) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Bounds for the Rate of Strong Approximation in the Multidimensional Invariance Principle

F. Götzea, A. Yu. Zaitsevb

a Bielefeld University, Department of Mathematics
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (1965 kB) Citations (15)
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DOI: https://doi.org/10.4213/tvp2484
Abstract: The goal of this paper is to derive consequences of the result of Zaitsev [Theory Probab. Appl., 45 (2001), pp. 624–642; 46 (2002), pp. 490–514; 676–698]. 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 $\mathbf{E}\|\xi_j\|^\gamma$, $\gamma\ge 2$. A multidimensional version of the results of Sakhanenko [Trudy Inst. Mat., 5 (1985), pp. 27–44 (in Russian)] is obtained.
Keywords: multidimensional invariance principle, strong approximation, sums of independent random vectors.
Received: 31.07.2007
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 1, Pages 59–80
DOI: https://doi.org/10.1137/S0040585X9798350X
Bibliographic databases:
Language: English
Citation: F. Götze, A. Yu. Zaitsev, “Bounds for the Rate of Strong Approximation in the Multidimensional Invariance Principle”, Teor. Veroyatnost. i Primenen., 53:1 (2008), 100–123; Theory Probab. Appl., 53:1 (2009), 59–80
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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