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Teor. Veroyatnost. i Primenen., 1982, Volume 27, Issue 2, Pages 279–285 (Mi tvp2345)  

Estimates of the accuracy of normal approximation in a Hilbert space

B. A. Zalesskiĭ

Moscow

Abstract: Let $X_1,X_2,…$ be a sequence of independent identically distributed random variables with values in a separable Hilbert space such that $\mathbf EX_j=0$, $\mathbf E|x_j|^{3+\delta}<\infty$, $0\le\delta\le 1$. Estimates of the accuracy of normal approximation for $\mathbf P\{|n^{-1/2}(X_1+…+X_n)|<r\}$ are constructed. For $0\le\delta\le 1$ the order of approximation is $O(n^{-1_+\delta)/2})$, for $\delta=1$ the order is $O(n^{-1+\varepsilon})$, $\varepsilon>0$.

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English version:
Theory of Probability and its Applications, 1983, 27:2, 290–298

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Received: 22.10.1981

Citation: B. A. Zalesskiǐ, “Estimates of the accuracy of normal approximation in a Hilbert space”, Teor. Veroyatnost. i Primenen., 27:2 (1982), 279–285; Theory Probab. Appl., 27:2 (1983), 290–298

Citation in format AMSBIB
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\by B.~A.~Zalesski{\v\i}
\paper Estimates of the accuracy of normal approximation in a~Hilbert space
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 2
\pages 279--285
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=657922}
\zmath{https://zbmath.org/?q=an:0565.60004}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 2
\pages 290--298
\crossref{https://doi.org/10.1137/1127031}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983QN71900007}


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