ISSN:
1436-5081
Keywords:
1991 Mathematics Subject Classification: 60G10
;
28D05
;
Key words: Finite dimensional distributions
;
ergodic Markov Chain
;
mixing Gaussian dynamical system
;
entropy
;
group rotation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s006050070034
Permalink
