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Random Stationary Processes

Kenneth S. Alexander and Steven A. Kalikow
The Annals of Probability
Vol. 20, No. 3 (Jul., 1992), pp. 1174-1198
Stable URL: http://www.jstor.org/stable/2244637
Page Count: 25
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Random Stationary Processes
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Abstract

Given a finite alphabet, there is an inductive method for constructing a stationary measure on doubly infinite words from this alphabet. This construction can be randomized; the main focus here is on a particular uniform randomization which intuitively corresponds to the idea of choosing a generic stationary process. It is shown that with probability 1, the random stationary process has zero entropy and gives positive probability to every periodic infinite word.

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