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. 
@article{THSP_2014_19_1_a7,
     author = {V. I. Senin},
     title = {Sojourn measures of random walks on deterministic sequences},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {91--99},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a7/}
}
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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/