Abstract:
The aim of this paper is to derive new optimal bounds for the rate of strong Gaussian approximation of sums of i.i.d. Rd-valued random variables ξj having finite moments of the form EH(|ξj|), where H(x) is a monotone function growing not slower than x2+δ and not faster than ecx. We obtain some generalizations of the results of U. Einmahl (1989). Bibl. – 44 titles.
Citation:
A. Yu. Zaitsev, “The rate of Gaussian strong approximation for the sums of i.i.d. multidimensional random vectors”, Probability and statistics. Part 14–2, Zap. Nauchn. Sem. POMI, 364, POMI, St. Petersburg, 2009, 148–165; J. Math. Sci. (N. Y.), 163:4 (2010), 399–408
\Bibitem{Zai09}
\by A.~Yu.~Zaitsev
\paper The rate of Gaussian strong approximation for the sums of i.i.d. multidimensional random vectors
\inbook Probability and statistics. Part~14--2
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 364
\pages 148--165
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3155}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 163
\issue 4
\pages 399--408
\crossref{https://doi.org/10.1007/s10958-009-9682-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70549109096}
Linking options:
https://www.mathnet.ru/eng/znsl3155
https://www.mathnet.ru/eng/znsl/v364/p148
This publication is cited in the following 8 articles:
G. A. Krylova, “The estimation of traffic intensity parameter for a single-channel queueing system with regenerative input flow”, Moscow University Mathematics Bulletin, 77:5 (2022), 242–246
Lifshits M.A. Nikitin Ya.Yu. Petrov V.V. Zaitsev A.Yu. Zinger A.A., “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
Hiroshi Takahashi, Shuya Kanagawa, Ken-ichi Yoshihara, “Asymptotic Behavior of Solutions of Some Difference Equations Defined by Weakly Dependent Random Vectors”, Stochastic Analysis and Applications, 33:4 (2015), 740
A. Yu. Zaitsev, “The accuracy of strong Gaussian approximation for sums of independent random vectors”, Russian Math. Surveys, 68:4 (2013), 721–761
F. Götze, A. Yu. Zaitsev, “Estimates for the rate of strong approximation in Hilbert space”, Siberian Math. J., 52:4 (2011), 628–638
A. I. Sakhanenko, “A general estimate in the invariance principle”, Siberian Math. J., 52:4 (2011), 696–710
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
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
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