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Markov chains with exponential return times are finitary

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  29 September 2020

OMER ANGEL  and
YINON SPINKA
OMER ANGEL
Affiliation:
Department of Mathematics, University of British Columbia 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada (e-mail: angel@math.ubc.ca; yinon@math.ubc.ca)
YINON SPINKA
Affiliation:
Department of Mathematics, University of British Columbia 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada (e-mail: angel@math.ubc.ca; yinon@math.ubc.ca)
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Abstract

Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an independent and identically distributed (i.i.d.) process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of ${\mathbb {Z}}$ is a finitary factor of an i.i.d. process.

Keywords

random dynamicssymbolic dynamicsfactor of iidfinitary codingMarkov chain

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60G10: Stationary processes
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 10 , October 2021 , pp. 2918 - 2926
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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