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Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 2, Pages 289–294 (Mi tvp845)  

Some remarks on multidimensional inegualities of the Bernstein–Kolmogorov type

V. M. Zolotarev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Let $X_1,…,X_n$ be independent random vectors in $R^m$ for which $\mathbf EX_i=0$ and $Y=X_1+…+X_n$. In the paper upper bounds of the type of the Bernstein–Kolmogorov inequalities are obtained for the probabilities $\mathbf P(|Y|\ge t)$ in case when the components of $X_i$'s form a Lévy martingale (in the sense of definition (3)) or when these vectors have spherical distributions. The orders of magnitude of the estimates obtained can not be improved.

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English version:
Theory of Probability and its Applications, 1968, 13:2, 281–286

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Received: 08.02.1968

Citation: V. M. Zolotarev, “Some remarks on multidimensional inegualities of the Bernstein–Kolmogorov type”, Teor. Veroyatnost. i Primenen., 13:2 (1968), 289–294; Theory Probab. Appl., 13:2 (1968), 281–286

Citation in format AMSBIB
\Bibitem{Zol68}
\by V.~M.~Zolotarev
\paper Some remarks on multidimensional inegualities of the Bernstein--Kolmogorov type
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 2
\pages 289--294
\mathnet{http://mi.mathnet.ru/tvp845}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=230352}
\zmath{https://zbmath.org/?q=an:0169.21002}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 2
\pages 281--286
\crossref{https://doi.org/10.1137/1113031}


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