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Teor. Veroyatnost. i Primenen., 1959, Volume 4, Issue 3, Pages 311–321 (Mi tvp4891)  

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

An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions

Yu. V. Linnik

Leningrad

Abstract: The proof is based on the “information functional” $-(\int_{-\infty}^{+\infty}{p(x)\ln p(x) dx}+\frac12\ln\mathbf D(x))$, $p(x)$ being the density of the random variable $X$. Some new dependencies between the Shannon and Fisher information quantities are established and an information theoretic interpretation of the Lindeberg condition is given.

Full text: PDF file (1016 kB)

English version:
Theory of Probability and its Applications, 1959, 4:3, 288–299

Received: 25.12.1958

Citation: Yu. V. Linnik, “An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions”, Teor. Veroyatnost. i Primenen., 4:3 (1959), 311–321; Theory Probab. Appl., 4:3 (1959), 288–299

Citation in format AMSBIB
\Bibitem{Lin59}
\by Yu.~V.~Linnik
\paper An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions
\jour Teor. Veroyatnost. i Primenen.
\yr 1959
\vol 4
\issue 3
\pages 311--321
\mathnet{http://mi.mathnet.ru/tvp4891}
\transl
\jour Theory Probab. Appl.
\yr 1959
\vol 4
\issue 3
\pages 288--299
\crossref{https://doi.org/10.1137/1104028}


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    This publication is cited in the following articles:
    1. A. S. Holevo, “Asymptotic estimation of a shift parameter of a quantum state”, Theory Probab. Appl., 49:2 (2005), 207–220  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Theory Probab. Appl., 50:2 (2006), 214–224  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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