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Mat. Zametki, 1968, Volume 3, Issue 6, Pages 731–738 (Mi mz6735)  

A probability inequality

A. V. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: The inequalities due to S. N. Bernshtein for the probability of $P(|Y_n|\ge r)$, where $|Y_n|$ is the length of the vector of the normalized sum of the independent and identically distributed vectors and $r>0$ is an arbitrary quantity are extended to the case of two and three dimensions. Some results are also given in the multidimensional case.

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English version:
Mathematical Notes, 1968, 3:6, 467–472

Bibliographic databases:

UDC: 519.2
Received: 15.03.1968

Citation: A. V. Prokhorov, “A probability inequality”, Mat. Zametki, 3:6 (1968), 731–738; Math. Notes, 3:6 (1968), 467–472

Citation in format AMSBIB
\Bibitem{Pro68}
\by A.~V.~Prokhorov
\paper A~probability inequality
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 6
\pages 731--738
\mathnet{http://mi.mathnet.ru/mz6735}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=231424}
\zmath{https://zbmath.org/?q=an:0199.52901}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 6
\pages 467--472
\crossref{https://doi.org/10.1007/BF01110608}


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