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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 1, Pages 156–160 (Mi tvp2479)  

This article is cited in 1 scientific paper (total in 2 paper)

Short Communications

On an estimate of the concentration function for the sum of identically distributed two-dimensional independent lattice random vectors

A. G. Postnikova, A. A. Judinb

a Moscow
b Vladimir

Abstract: The following theorem is proved. If $\xi_1,\xi_2,…$ is a sequence of non-degenerate identically distributed independent random variables with values in $Z^2$, then
$$ \sup_{m\in Z^2}\mathbf P(\xi_1+…+\xi_n=m)\le Cn^{-1}\Delta^{-1/2}, $$
where $C$ is an absolute constant, $\Delta=(P_L-P_0)(1-P_L)$,
$$ P_0=\max_{m\in Z^2}\mathbf P\{\xi=x\},\qquad P_L=\max_H\mathbf P\{\xi\in H\}, $$
$H$ is a set of points belonging to some straight line.

Full text: PDF file (269 kB)

English version:
Theory of Probability and its Applications, 1981, 26:1, 152–156

Bibliographic databases:

Received: 31.10.1978

Citation: A. G. Postnikov, A. A. Judin, “On an estimate of the concentration function for the sum of identically distributed two-dimensional independent lattice random vectors”, Teor. Veroyatnost. i Primenen., 26:1 (1981), 156–160; Theory Probab. Appl., 26:1 (1981), 152–156

Citation in format AMSBIB
\Bibitem{PosYud81}
\by A.~G.~Postnikov, A.~A.~Judin
\paper On an estimate of the concentration function for the sum of identically distributed two-dimensional independent lattice random vectors
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 1
\pages 156--160
\mathnet{http://mi.mathnet.ru/tvp2479}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=605645}
\zmath{https://zbmath.org/?q=an:0473.60024|0454.60016}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 26
\issue 1
\pages 152--156
\crossref{https://doi.org/10.1137/1126014}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MY89200014}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Vladimirov, A. A. Dezin, A. A. Karatsuba, L. D. Kudryavtsev, M. P. Mineev, S. M. Nikol'skii, L. P. Postnikova, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, A. A. Yudin, “Aleksei Georgievich Postnikov (obituary)”, Russian Math. Surveys, 53:1 (1998), 199–204  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. B. Khripunova, A. A. Yudin, “Estimate of the Concentration Function for a Class of Additive Functions”, Math. Notes, 82:4 (2007), 535–541  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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