On finitary shifts

M. BINKOWSKA; B. KAMINSKI

doi:10.2969/jmsj/04930487

On finitary shifts

M. BINKOWSKA, B. KAMINSKI

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Keywords: finitary processes, finitary shifts, euclidean representation, spectral representation

JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 487-500

DOI https://doi.org/10.2969/jmsj/04930487

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Published: 1997 Received: June 07, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: KEYWORD Details: Right : finitary processes, finitary shifts, euclidean representation, spectral representation

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Adler, P. Shields and M. Smorodinsky, Irreducible Markov shifts, Ann. Math. Statist., 43 (1972), 1072-1029.
2) M. Binkowska, Weak mixing finitary shifts are Bernouli, Bull. Polish Acad. Sci. Math., 32 (1984), 185-191.
3) M. Binkowska, An example of a weak Bernoulli process which is not finitary, Colloq. Math., 59 (1990), 151-156.
4) M. Binkowska and B. Kaminski, Classification of ergodic finitary shifts, Ann. Sci. Univ. Clermont-Ferrand II. Probab. Appl., 2 (1984), 25-37.
5) A. Heller, On stochastic processes derived from Markov chains, Ann. Math. Statist., 30 (1959), 688-697.
6) J. Kubo, H. Murata and H. Totoki, On the isomorphism problem for endomorphisms of Lebesque spaces I, II, Publs. RIMS, Kyoto Univ., 9 (1974), 285-296.
7) D. S. Ornstein, Ergodic Theory, Radomness and Dynamical Systems, New Haven and London, Yale University Press, (1974).
8) J. B. Robertson, A spectral representation of the states of a measure preserving transformation, Z. Wahrsch. Verw. Gebiete, 27 (1974), 185-194.
9) J. B. Robertson, The mixing properties of certain processes related to Markov chains, Math. Systems Theory, 7 (1973), 39-43.

Right : [1] R. Adler, P. Shields and M. Smorodinsky, Irreducible Markov shifts, Ann. Math. Statist., 43 (1972), 1072-1029.
[2] M. Binkowska, Weak mixing finitary shifts are Bernouli, Bull. Polish Acad. Sci. Math., 32 (1984), 185-191.
[3] M. Binkowska, An example of a weak Bernoulli process which is not finitary, Colloq. Math., 59 (1990), 151-156.
[4] M. Binkowska and B. Kaminski, Classification of ergodic finitary shifts, Ann. Sci. Univ. Clermont-Ferrand II. Probab. Appl., 2 (1984), 25-37.
[5] A. Heller, On stochastic processes derived from Markov chains, Ann. Math. Statist., 30 (1959), 688-697.
[6] J. Kubo, H. Murata and H. Totoki, On the isomorphism problem for endomorphisms of Lebesque spaces I, II, Publs. RIMS, Kyoto Univ., 9 (1974), 285-296.
[7] D. S. Ornstein, Ergodic Theory, Radomness and Dynamical Systems, New Haven and London, Yale University Press, (1974).
[8] J. B. Robertson, A spectral representation of the states of a measure preserving transformation, Z. Wahrsch. Verw. Gebiete, 27 (1974), 185-194.
[9] J. B. Robertson, The mixing properties of certain processes related to Markov chains, Math. Systems Theory, 7 (1973), 39-43.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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