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Zbl 0565.60059
Binkowska, M.; Kaminski, B.
Classification of ergodic finitary shifts. (English)
[J] Ann. Sci. Univ. Clermont-Ferrand II 78, Probab. Appl. 2, 26-37 (1984). ISSN 0246-1501

From the authors' introduction: {\it R. L. Adler}, {\it P. Shields} and the reviewer [Ann. Math. Stat. 43, 1027-1029 (1972; Zbl 0244.60053)] have shown that every irreducible finite state Markov shift is isomorphic to a direct product of a rotation and a Bernoulli shift. \par In this paper this result is extend to a wider class of shifts, the so called finitary shifts. These shifts are induced by finitary processes defined by {\it A. Heller} [ibid. 36, 1286-1291 (1965; Zbl 0139.346)]. He proved that these processes include Markov chains and also functionals of Markov chains and gave an example of a process which is finitary and is not a functional of a Markov chain.
[M.Smorodinsky]

MSC 2000:: *60J10 Markov chains with discrete parameter
28D05 Measure-preserving transformations

Keywords: Markov shift; Bernoulli shift; functionals of Markov chains

Citations: Zbl 0244.60053; Zbl 0139.346

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