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Probl. Peredachi Inf., 2017, Volume 53, Issue 3, Pages 16–22 (Mi ppi2239)  

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

Information Theory

On coupling of probability distributions and estimating the divergence through variation

V. V. Prelov

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: Let $X$ be a discrete random variable with a given probability distribution. For any $\alpha$, $0\le\alpha\le1$, we obtain precise values for both the maximum and minimum variational distance between $X$ and another random variable $Y$ under which an $\alpha$-coupling of these random variables is possible. We also give the maximum and minimum values for couplings of $X$ and $Y$ provided that the variational distance between these random variables is fixed. As a consequence, we obtain a new lower bound on the divergence through variational distance.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.


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English version:
Problems of Information Transmission, 2017, 53:3, 215–221

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 22.11.2016
Revised: 10.02.2017

Citation: V. V. Prelov, “On coupling of probability distributions and estimating the divergence through variation”, Probl. Peredachi Inf., 53:3 (2017), 16–22; Problems Inform. Transmission, 53:3 (2017), 215–221

Citation in format AMSBIB
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\by V.~V.~Prelov
\paper On coupling of probability distributions and estimating the divergence through variation
\jour Probl. Peredachi Inf.
\yr 2017
\vol 53
\issue 3
\pages 16--22
\mathnet{http://mi.mathnet.ru/ppi2239}
\elib{http://elibrary.ru/item.asp?id=29966406}
\transl
\jour Problems Inform. Transmission
\yr 2017
\vol 53
\issue 3
\pages 215--221
\crossref{https://doi.org/10.1134/S0032946017030024}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412936700002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85031709658}


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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. V. V. Prelov, “Optimal upper bounds for the divergence of finite-dimensional distributions under a given variational distance”, Problems Inform. Transmission, 55:3 (2019), 218–225  mathnet  crossref  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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