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Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 2, Pages 318–326 (Mi tvp377)  

On Isomorphism Problem of Stationary Processes

A. H. Zaslavskiĭ

Novosibirsk

Abstract: The central problem in ergodic theory is that of isomorphism. In the paper the sufficient condition for isomorphism of the stationary process $\xi=(…,\xi_{-1},\xi_0,\xi_1,…)$, $\xi_n=0$, $1,…,l$, with some stationary process $\eta=(…,\eta_{-1},\eta_0,\eta_1,…)$, $\eta_n=\alpha_1,…,\alpha_m$, $m\leqq l$, is found. This condition is expressed in terms of a one-dimensional distribution of the process $\xi$. Isomorphism is constructed with the aid of elementary codes
$$ (i)=\eta_1^i\eta_2^i\cdots\eta_{\omega_i}^i,\qquad i=1,…,l, $$
which code the elementary words
$$ (i)=\underbrace{i00…0}_{\omega_i}. $$
One of the examples considered proves that it is possible to construct a system of elementary codes for any arbitrary $l$ and $m$. This system possesses some properties which secure unique decoding of the sequence $\eta$.

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English version:
Theory of Probability and its Applications, 1964, 9:2, 291–298

Bibliographic databases:

Received: 31.08.1962

Citation: A. H. Zaslavskiǐ, “On Isomorphism Problem of Stationary Processes”, Teor. Veroyatnost. i Primenen., 9:2 (1964), 318–326; Theory Probab. Appl., 9:2 (1964), 291–298

Citation in format AMSBIB
\Bibitem{Zas64}
\by A.~H.~Zaslavski{\v\i}
\paper On Isomorphism Problem of Stationary Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 2
\pages 318--326
\mathnet{http://mi.mathnet.ru/tvp377}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=164377}
\zmath{https://zbmath.org/?q=an:0154.18901}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 2
\pages 291--298
\crossref{https://doi.org/10.1137/1109041}


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