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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 4, Pages 835–841 (Mi tvp3515)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the smoothing of probabilities for the sums of integer valued random variables

N. G. Gamkrelidze

Tbilisi

Abstract: Let $\xi_1,\xi_2,…$ be integer valued independent random variables and $S_n=\xi_1+…+\xi_n$. We introduce the function
$$ \sum_m|\mathbf P\{S_n=m\}-\mathbf P\{S_n=m-1\}| $$
as a measure of the «smoothness» of the distribution $S_n$. Some properties of this function are investigated.

Full text: PDF file (1674 kB)

English version:
Theory of Probability and its Applications, 1982, 26:4, 823–828

Bibliographic databases:

Received: 06.05.1980

Citation: N. G. Gamkrelidze, “On the smoothing of probabilities for the sums of integer valued random variables”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 835–841; Theory Probab. Appl., 26:4 (1982), 823–828

Citation in format AMSBIB
\Bibitem{Gam81}
\by N.~G.~Gamkrelidze
\paper On the smoothing of probabilities for the sums of integer valued random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 835--841
\mathnet{http://mi.mathnet.ru/tvp3515}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=636780}
\zmath{https://zbmath.org/?q=an:0501.60027|0491.60020}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 823--828
\crossref{https://doi.org/10.1137/1126091}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PM42700017}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Theory Probab. Appl., 56:2 (2011), 350–358  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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