Geodesic
Local visitation measures for some sequences of random variables with
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 155-164 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the sequence of equally distributed random variables $\{x_n,\ n\ge 1\}$, satisfying some mixing condition, the local visitation measures of the sequences $\{x_n/a_n,\ n\ge 1\}$ are considered with various real sequences $\{a_n,\ n\ge 1\}$ tending monotonically to 0. We give sufficient conditions for the measures $\{\sum_{k=1}^n P(x_k/a_k)^{-1},\ n\ge 1\}$ to be the local visitation measures for $\{x_n/a_n,\ n\ge 1\}$ with probability 1.
Keywords: local visitation measures, mixing. 
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M. A. Vlasenko. Local visitation measures for some sequences of random variables with. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 155-164. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a8/

[1] Ukrainian Math. J., 48:8, 1182–1201, 1997, MR 98f:60126 | DOI | MR | Zbl

[2] Ukrainian Math. J., 51:1 (1999), 134–139, MR 2001f:60039 | DOI | DOI | MR | Zbl

[3] Dorogovtsev A. A., Denis'evskij N. A., “Path-wise behaviour of stationary sequences”, Theory Stochastic Process., 2(18):3–4 (1996), 17–26 | MR | Zbl

[4] Bryc W., Smoleński W., “Moment conditions for almost sure convergence of weakly correlated random variables”, Proc. Amer. Math. Soc., 119:2 (1993), 629–635 | DOI | MR | Zbl

[5] Kuipers L., Niederreiter H., Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley Sons], New York, London, Sydney, 1974, xiv+390 pp. | MR | Zbl

[6] Dorogovtsev A. Ya., Mathematical analysis, v. 1, Lybid', Kyiv, 1993

[7] Billinsley P., Convergence of probability measures, John Wiley Sons, Inc., New York, London, Sydney, 1968, xii+253 pp. | MR