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A note on roots of Markov shifts

Published online by Cambridge University Press:  14 July 2016

S. M. Rudolfer
S. M. Rudolfer*
Affiliation:
University of Manchester
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Abstract

Let Tv be the two-sided shift operator associated with a finite Markov chain of period v; Using results of Krengel and Michel and Adler, Shields and Smorodinsky, necessary and sufficient conditions for the existence of an rth root of Tv are obtained. In particular, if the Markov chain is irreducible, then Tv has an rth root when and only when (r, v) = 1.

Keywords

ROOTS OF TRANSFORMATIONSMARKOV SHIFTSBERNOULLI SHIFTSIMBEDDING TRANSFORMATIONS IN FLOWSERGODIC AUTOMORPHISMS WITH DISCRETE SPECTRUMK-AUTOMORPHISMSENTROPYCOMPLETE METRIC INVARIANTSTOCHASTIC PROCESSCARTESIAN PRODUCTROTATION ON A CYCLIC GROUP
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 591 - 596
Copyright
Copyright © Applied Probability Trust 1976 

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References

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