|
Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 4, Pages 678–697
(Mi tvp754)
|
|
|
|
This article is cited in 5 scientific papers (total in 5 papers)
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 $x_1(\omega),\dots,x_n(\omega)$, are independent random variables on a group $G$ then for $z_n(\omega)=x_1(\omega),\dots,x_n(\omega)$ 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 $x_1(\omega),\dots,x_n(\omega),\dots$ converge.
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
Linking options:
https://www.mathnet.ru/eng/tvp754 https://www.mathnet.ru/eng/tvp/v12/i4/p678
|
|