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Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 4, Pages 734–744 (Mi tvp1228)  

This article is cited in 8 scientific papers (total in 8 papers)

On the estimates of the rate of convergence in the invariance principle for Banach spaces

A. A. Borovkov, A. I. Sahanenko

Novosibirsk

Abstract: We propose a method for obtaining the estimates in the invariance principle for Banach spaces; this method doesn't use the representation on a common probability space. In particular, it is shown that the estimate proved by Borovkov [7] for the one- dimensional invariance principle remains valid for the finite-dimensional case too.

Full text: PDF file (629 kB)

English version:
Theory of Probability and its Applications, 1981, 25:4, 721–731

Bibliographic databases:

Received: 03.04.1980

Citation: A. A. Borovkov, A. I. Sahanenko, “On the estimates of the rate of convergence in the invariance principle for Banach spaces”, Teor. Veroyatnost. i Primenen., 25:4 (1980), 734–744; Theory Probab. Appl., 25:4 (1981), 721–731

Citation in format AMSBIB
\Bibitem{BorSak80}
\by A.~A.~Borovkov, A.~I.~Sahanenko
\paper On the estimates of the rate of convergence in the invariance principle for Banach spaces
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 4
\pages 734--744
\mathnet{http://mi.mathnet.ru/tvp1228}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=595135}
\zmath{https://zbmath.org/?q=an:0471.60039|0454.60033}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 4
\pages 721--731
\crossref{https://doi.org/10.1137/1125087}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980MK50200005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Borovkov, “Boundary-value problems, the invariance principle, and large deviations”, Russian Math. Surveys, 38:4 (1983), 259–290  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Zaitsev, “Estimates for the rate of strong Gaussian approximation for the sums of i.i.d. multidimensional random vectors”, J. Math. Sci. (N. Y.), 152:6 (2008), 875–884  mathnet  crossref
    3. Theory Probab. Appl., 53:1 (2009), 59–80  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. 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
    5. 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
    6. 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
    7. 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
    8. F. Gettse, A. Yu. Zaitsev, D. N. Zaporozhets, “Uluchshennyi mnogomernyi variant vtoroi ravnomernoi predelnoi teoremy Kolmogorova”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 71–85  mathnet
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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