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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 193–195 (Mi tvp2695)  

Short Communications

On sums of random vectors

A. V. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: In the paper one variant of multidimensional analogues of the Bernstein–Kolmogorov inequalities is proposed. Let $X_1,…,X_n$ be identically distributed independent random vectors in $R^m$, for which $\mathbf EX_i=0$, $|X_i|<L$, $Y_n=\sum X_j/\sqrt n$. Assuming that eigenvalues of covariance matrix of $X_i$ are equal $\lambda_1=…=\lambda_m=\lambda$ we prove inequality (2) for $\mathbf P(|Y_n|>\rho\sqrt\lambda)$.

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English version:
Theory of Probability and its Applications, 1973, 18:1, 186–188

Bibliographic databases:

Received: 20.10.1971

Citation: A. V. Prokhorov, “On sums of random vectors”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 193–195; Theory Probab. Appl., 18:1 (1973), 186–188

Citation in format AMSBIB
\Bibitem{Pro73}
\by A.~V.~Prokhorov
\paper On sums of random vectors
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 193--195
\mathnet{http://mi.mathnet.ru/tvp2695}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=312546}
\zmath{https://zbmath.org/?q=an:0292.60080}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 186--188
\crossref{https://doi.org/10.1137/1118019}


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