Abstract.
We prove that if is a finite valued stationary Markov Chain with strictly positive probability transitions, then for any natural number p, there exists a continuum of finite valued non Markovian processes which have the p-marginal distributions of X and with positive entropy, whereas for an irrational rotation and essentially bounded real measurable function f with no zero Fourier coefficient on the unit circle with normalized Lebesgue measure, the process is uniquely determined by its three-dimensional distributions in the class of ergodic processes. We give also a family of Gaussian non-Markovian dynamical systems for which the symbolic dynamic associated to the time zero partition has the two-dimensional distributions of a reversible mixing Markov Chain.
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(Received 22 July 1999; in revised form 24 February 2000)
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Hamdan, D. Markov Chains with Positive Transitions Are Not Determined by Any p-Marginals. Mh Math 130, 189–199 (2000). https://doi.org/10.1007/s006050070034
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DOI: https://doi.org/10.1007/s006050070034