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This article is cited in 2 scientific papers (total in 2 papers)
Conditions for the limit distribution equiprobability in a linear autoregression scheme with random control on a finite group
I. A. Kruglov
Abstract:
We consider the sequence of random variables
$$
\mu^{(N)}=\xi_N(\mu^{(N-1)})^{\zeta_N},
\qquad
N=1,2,\dots,
$$
where $\mu^{(0)}$ is a random variable that takes values in a finite group
$G=(G, \bullet)$, $(\xi_N, \zeta_N)$, $N=1,2,\dots$,
is a sequence of identically distributed random variables that take values
in the Cartesian product $G\times\operatorname{Aut}G$, where $(\operatorname{Aut}G, \circ)$
is the group of automorphisms of $G$. We assume that the random variables
$\mu^{(0)}$, $(\xi_N, \zeta_N)$, $N=1,2,\dots$, are independent.
Given an arbitrary distribution of $\mu^{(0)}$,
we find general necessary and sufficient conditions for the convergence, as $N\to\infty$,
of the sequence of distributions of random variables $\mu^{(N)}$
to the equiprobable on $G$ distribution.
This research was supported by the Program of the President of the Russian Federation
for supporting the leading scientific schools, grant 2358.2003.9.
Received: 15.12.2004
Citation:
I. A. Kruglov, “Conditions for the limit distribution equiprobability in a linear autoregression scheme with random control on a finite group”, Diskr. Mat., 17:3 (2005), 12–18; Discrete Math. Appl., 15:4 (2005), 387–393
Linking options:
https://www.mathnet.ru/eng/dm112https://doi.org/10.4213/dm112 https://www.mathnet.ru/eng/dm/v17/i3/p12
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