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I. A. Kruglov

Conditions for asymptotic equiprobability of distributions in stochastically controlled linear autoregressions over a finite group

We consider the sequence of random variables

μ^(N) = ξ_N (μ ^(N−1))^ζN , N = 1,2, . . . ,

where μ⁽⁰⁾ is a random variable that takes values in a finite group G = (G, •), (ξ_N, ζ_N), N = 1,2, . . . , is a sequence of identically distributed random variables that take values in the Cartesian product G × Aut G, Where (Aut G, ∘) is the group of automorphisms of G. We assume that the random variables μ⁽⁰⁾, (ξ_N, ζ_N), N = 1,2, . . . , are independent. Given an arbitrary distribution of μ⁽⁰⁾, we find general necessary and sufficient conditions for the convergence, as N → ∞, of the sequence of distributions of random variables μ^(N) to the equiprobable on G distribution.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 15, 05/2005
Pages: 387 - 393

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