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Applications of Ornstein's theory to stationary processes

Part of the Lecture Notes in Mathematics book series (LNM,volume 330)

Keywords

  • Spectral Measure
  • Isomorphism Problem
  • Bernoulli Shift
  • Gaussian Stationary Process
  • Markov Shift

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References

  1. Ибрагимов, И. А. и Ю. В. Линник, Независимые и стачионарно связанные величины, Изд. Наука, Москва, 1965.

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  2. Ornstein, D., Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4(1970), 337–352.

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  3. __, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5(1971), 339–348.

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  4. __, Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5(1971), 349–364.

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  5. Friedman N. and D. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5(1971), 365–394.

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  6. Ornstein, D., A Kolmogorov automorphism that is not a Bernoulli shift.

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  7. McCabe R. and P. Shields, A class of Markov shifts which are Bernoulli shifts, Advances in Math. 6(1971), 323–328.

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  8. Maruyama G., Some aspects of Orntein's theory of isomorphism problems in ergodic theory, Pub. Res. Inst. Math. Sci., 7(1972), 511–539.

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© 1973 Springer-Verlag

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Maruyama, G. (1973). Applications of Ornstein's theory to stationary processes. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061495

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  • DOI: https://doi.org/10.1007/BFb0061495

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06358-2

  • Online ISBN: 978-3-540-46956-8

  • eBook Packages: Springer Book Archive