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 is a finitary factor of an i.i.d. process.
Original language | English |
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Pages (from-to) | 2918-2926 |
Number of pages | 9 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 41 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2021 |
Externally published | Yes |
Keywords
- Factor of iid
- Finitary coding
- Markov chain
- Random dynamics
- Symbolic dynamics
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- General Mathematics