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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 4, Pages 678–697 (Mi tvp754)  

On convergence of the products of independents random variables on a finite group

V. M. Maksimov

Moscow

Abstract: The notion of variance for random variables on a finite group $G$ as a numerical function is axiomatically introduced. The variance is applied to study questions of convergence of the product of random variables on $G$. In particular the following theorem is proved: if $x_1(\omega),…,x_n(\omega)$, are independent random variables on a group $G$ then for $z_n(\omega)=x_1(\omega),…,x_n(\omega)$ to converge almost everywhere the necessary and sufficient conditions are that distributions of $x_n(\omega)$ tend to the distribution concentrated on the unit of $G$ and the series of variances for the sequence $x_1(\omega),…,x_n(\omega),…$ converge.

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English version:
Theory of Probability and its Applications, 1967, 12:4, 619–637

Bibliographic databases:

Received: 13.05.1966

Citation: V. M. Maksimov, “On convergence of the products of independents random variables on a finite group”, Teor. Veroyatnost. i Primenen., 12:4 (1967), 678–697; Theory Probab. Appl., 12:4 (1967), 619–637

Citation in format AMSBIB
\Bibitem{Mak67}
\by V.~M.~Maksimov
\paper On convergence of the products of independents random variables on a~finite group
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 4
\pages 678--697
\mathnet{http://mi.mathnet.ru/tvp754}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=228026}
\zmath{https://zbmath.org/?q=an:0178.18803}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 4
\pages 619--637
\crossref{https://doi.org/10.1137/1112077}


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