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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 1, Pages 100–123 (Mi tvp2484)  

This article is cited in 9 scientific papers (total in 9 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

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.

DOI: https://doi.org/10.4213/tvp2484

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English version:
Theory of Probability and its Applications, 2009, 53:1, 59–80

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Received: 31.07.2007
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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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Yu. Zaitsev, “The rate of Gaussian strong approximation for the sums of i.i.d. multidimensional random vectors”, J. Math. Sci. (N. Y.), 163:4 (2010), 399–408  mathnet  crossref
    2. F. Götze, A. Yu. Zaitsev, “Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments”, J. Math. Sci. (N. Y.), 167:4 (2010), 495–500  mathnet  crossref  mathscinet
    3. F. Götze, A. Yu. Zaitsev, “Estimates for the rate of strong approximation in Hilbert space”, Siberian Math. J., 52:4 (2011), 628–638  mathnet  crossref  mathscinet  isi
    4. A. Yu. Zaitsev, “Optimal estimates for the rate of strong Gaussian approximation in the infinite dimensional invariance principle”, J. Math. Sci. (N. Y.), 188:6 (2013), 689–693  mathnet  crossref  mathscinet
    5. A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721–761  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Trapani L., “Comments on: Extensions of Some Classical Methods in Change Point Analysis Discussion”, Test, 23:2 (2014), 283–286  crossref  mathscinet  zmath  isi  scopus
    7. Berkes I., Liu W., Wu W.B., “Komlos-Major-Tusnady Approximation Under Dependence”, Ann. Probab., 42:2 (2014), 794–817  crossref  mathscinet  zmath  isi  elib  scopus
    8. Merlevede F., Rio E., “Strong Approximation For Additive Functionals of Geometrically Ergodic Markov Chains”, Electron. J. Probab., 20 (2015), 1–27  crossref  mathscinet  isi  scopus
    9. M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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