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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 4, Pages 715–724 (Mi tvp2219)

On the preservation of statistical properties for subsequences of random sequences

D. B. Sten'kin

Moscow

Abstract: Let $X$ be a one-sided sequence space and $\mathbf P$ be a probability measure on $X$ invariant under the shift transformation $T$ and such that the coordinates $x_i$ of $x\in X$ are weakly dependent. It is well-known that $\mathbf P$-almost every point $x\in X$ is $\mathbf P$-normal, i. e. for any sufficiently good $A\subset X$
$$\lim_{n\to\infty}n^{-1}\operatorname{card}\{i:T^ix\in A, i\le n\}=\mathbf P(A).$$
We find conditions on the integer-valued sequence $\tau=(\tau_0,\tau_1,…)$ under which the normality of a point $x=(x_0,x_1,…)\in X$ s X implies that of the point $x'=(x_{\tau_0},x_{\tau_1},…)$.

Full text: PDF file (545 kB)

English version:
Theory of Probability and its Applications, 1984, 28:3, 752–761

Bibliographic databases:

Citation: D. B. Sten'kin, “On the preservation of statistical properties for subsequences of random sequences”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 715–724; Theory Probab. Appl., 28:3 (1984), 752–761

Citation in format AMSBIB
\Bibitem{Ste83} \by D.~B.~Sten'kin \paper On the preservation of statistical properties for subsequences of random sequences \jour Teor. Veroyatnost. i Primenen. \yr 1983 \vol 28 \issue 4 \pages 715--724 \mathnet{http://mi.mathnet.ru/tvp2219} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=726897} \zmath{https://zbmath.org/?q=an:0544.60002|0522.60003} \transl \jour Theory Probab. Appl. \yr 1984 \vol 28 \issue 3 \pages 752--761 \crossref{https://doi.org/10.1137/1128073} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700009}