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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 396, Pages 93–101 (Mi znsl4653)  
This article is cited in 3 scientific papers (total in 3 papers)

Optimal estimates for the rate of strong Gaussian approximation in the infinite dimensional invariance principle

A. Yu. Zaitsevab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (568 kB) Citations (3)
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Abstract: Estimates for the rate of strong Gaussian approximation in the invariance principle in the Hilbert space for sums of i.i.d. random vectors are derived. It is shown that they are optimal with respect to the order if the sequence of eigenvalues of the covariance operator of summands decreases slowly.
Key words and phrases: invariance principle, strong approximation, convergence rates, Hilbert space, sums of independent random vectors.
Received: 25.11.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 188, Issue 6, Pages 689–693
DOI: https://doi.org/10.1007/s10958-013-1159-2
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: A. Yu. Zaitsev, “Optimal estimates for the rate of strong Gaussian approximation in the infinite dimensional invariance principle”, Probability and statistics. Part 17, Zap. Nauchn. Sem. POMI, 396, POMI, St. Petersburg, 2011, 93–101; J. Math. Sci. (N. Y.), 188:6 (2013), 689–693
Citation in format AMSBIB
\Bibitem{Zai11}
\by A.~Yu.~Zaitsev
\paper Optimal estimates for the rate of strong Gaussian approximation in the infinite dimensional invariance principle
\inbook Probability and statistics. Part~17
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 396
\pages 93--101
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4653}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2870134}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 6
\pages 689--693
\crossref{https://doi.org/10.1007/s10958-013-1159-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880641565}
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  • https://www.mathnet.ru/eng/znsl/v396/p93
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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