Finitary codings and weak Bernoulli partitions
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- by A. del Junco and M. Rahe PDF
- Proc. Amer. Math. Soc. 75 (1979), 259-264 Request permission
Abstract:
An example is constructed of a two state stationary stochastic process (T, P) whose time zero partition P is weak Bernoulli under the shift, but which cannot be the image under a finitary coding of any independent process. A sufficient condition for a partition to be weak Bernoulli is developed, based on the rate of convergence of the conditional entropy $h(P|P_{ - j}^{ - 1})$ to $h(P,T)$.References
- M. A. Akcoglu, A. del Junco, and M. Rahe, Finitary codes between Markov processes, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 305–314. MR 525312, DOI 10.1007/BF00535166
- Rufus Bowen, Smooth partitions of Anosov diffeomorphisms are weak Bernoulli, Israel J. Math. 21 (1975), no. 2-3, 95–100. MR 385927, DOI 10.1007/BF02760788 D. S. Ornstein, personal communication.
- Meir Smorodinsky, A partition on a Bernoulli shift which is not weakly Bernoulli, Math. Systems Theory 5 (1971), 201–203. MR 297971, DOI 10.1007/BF01694176
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 259-264
- MSC: Primary 28D05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0532147-2
- MathSciNet review: 532147