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Teoriya Veroyatnostei i ee Primeneniya, 1964, Volume 9, Issue 2, Pages 318–326
(Mi tvp377)
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This article is cited in 2 scientific papers (total in 2 papers)
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 $\xi=(\dots,\xi_{-1},\xi_0,\xi_1,\dots)$, $\xi_n=0$, $1,\dots,l$, with some stationary process $\eta=(\dots,\eta_{-1},\eta_0,\eta_1,\dots)$, $\eta_n=\alpha_1,\dots,\alpha_m$, $m\leqq l$, 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
$$
(i)=\eta_1^i\eta_2^i\cdots\eta_{\omega_i}^i,\qquad i=1,\dots,l,
$$
which code the elementary words
$$
(i)=\underbrace{i00\dots 0}_{\omega_i}.
$$
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 $\eta$.
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
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