Geodesic
Sojourn measures of random walks on deterministic sequences
Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 91-99.

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We prove that for some class of random walks $\{Z(n),\,n\geq 0\}$, the random sequence $x_{Z(n)}$ almost surely inherits the property of a deterministic sequence $x_n$ to be uniformly distributed.
Keywords: Uniform distribution, random walk. 
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V. I. Senin. Sojourn measures of random walks on deterministic sequences. Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 91-99. http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a7/

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