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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 1, Pages 3–17 (Mi tvp946)  

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

A new version of the law of large numbers

V. N. Tutubalin

Moscow
Full-text PDF (878 kB) Citations (1)
Abstract: In this paper the system (0.1) of $N$ differential equations with random coefficients $\eta_{kj}(z)$ is considered. This system of coupled mode propagation is a mathematical model for wave-guides with random imperfections. The sum
\begin{equation} \sum_{j=1}^N |E_j(z)|^2 \end{equation}
is the power flow at the output of the wave-guide ($z$ is its lehgth). The physical considerations justify the investigation of an asymptotic problem when $N\to\infty$, $\eta_{kj}(z)\to 0$, $\alpha_j\to 0$, $z\to\infty$. Under some conditions the variance of the sum (1) converges to 0, while its expectation remains positive.
Received: 17.10.1977
English version:
Theory of Probability and its Applications, 1979, Volume 24, Issue 1, Pages 1–15
DOI: https://doi.org/10.1137/1124001
Bibliographic databases:
Language: Russian
Citation: V. N. Tutubalin, “A new version of the law of large numbers”, Teor. Veroyatnost. i Primenen., 24:1 (1979), 3–17; Theory Probab. Appl., 24:1 (1979), 1–15
Citation in format AMSBIB
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\by V.~N.~Tutubalin
\paper A new version of the law of large numbers
\jour Teor. Veroyatnost. i Primenen.
\yr 1979
\vol 24
\issue 1
\pages 3--17
\mathnet{http://mi.mathnet.ru/tvp946}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=522233}
\zmath{https://zbmath.org/?q=an:0432.60077|0396.60099}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 24
\issue 1
\pages 1--15
\crossref{https://doi.org/10.1137/1124001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JX60900001}
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  • https://www.mathnet.ru/eng/tvp/v24/i1/p3
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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