Abstract
Using Thouvenot’s relativized isomorphism theory, the author develops a conditionalized version of the Friedman—Ornstein result on Markov processes. This relativized statement is used to study the way in which a factor generated by a finite length stationary coding sits in a Markov process. All such factors split off if they are maximal in entropy. Moreover, one can show that if a finite coding factor fails to split off, it is relatively finite in a larger factor which either generates or itself splits off.
Similar content being viewed by others
References
N. A. Friedman and D. S. Ornstein,On isomorphism of weak Bernoulli transformations, Advances in Math.5 (1970), 365–394.
D. S. Ornstein,Factors of Bernoulli shifts, Israel J. Math.21 (1975), 145–153.
M. Rahe,Relatively finitely determined implies relatively very weak Bernoulli, Canad. J. Math.30 (1978), 531–548.
J.-P. Thouvenot,Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l’un est un schèma de Bernoulli Israel J. Math.21 (1975), 177–207.
J.-P. Thouvenot,Remarques sur les systèmes dynamiques donnes avec plusiers facteurs, Israel J. Math.21 (1975), 215–232.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rahe, M. Finite coding factors of Markov generators. Israel J. Math. 32, 349–355 (1979). https://doi.org/10.1007/BF02760463
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02760463