Finite coding factors of Markov generators
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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.
KeywordsMarkov Process Conditional Independence Large Factor Bernoulli Shift Converse Direction
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