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July, 1992 Random Stationary Processes
Kenneth S. Alexander, Steven A. Kalikow
Ann. Probab. 20(3): 1174-1198 (July, 1992). DOI: 10.1214/aop/1176989685


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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Kenneth S. Alexander. Steven A. Kalikow. "Random Stationary Processes." Ann. Probab. 20 (3) 1174 - 1198, July, 1992.


Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0766.60043
MathSciNet: MR1175256
Digital Object Identifier: 10.1214/aop/1176989685

Primary: 60G10
Secondary: 28D05 , 60G57

Keywords: Entropy , random measure , stationary process

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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