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I. A. Kruglov

Random sequences of the form X_t+1 = a_t X_t + b_t modul

In this paper, we prove inequalities for the mean square deviation δ_N,n of the N step transition matrix from the equiprobable matrix for certain random affine walk in the residue ring modulo n with dependent linear and drift components.

It is proved that the relation

is true if and only if N/n² → ∞ as n → ∞. Under this condition,

as n → ∞, where ε_n = 2 if n is even and ε_n = 1 if n is odd, l_n = n/2 if n is even and l_n = n if n is odd.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 15, 04/2005
Pages: 145 - 151

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