### Sojourn measures of random walks on deterministic sequences

**V. I. Senin**

*Theory of Stochastic Processes*

*Vol.19 (35), no.1, 2014, pp.91-99*

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.