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positive Harris recurrent, aperiodic, stationary Markov chain

If $X$ is Harris recurrent and aperiodic then $X$ is $\beta$-mixing (Theorem 3.5), and hence $\alpha$-mixing (Section 2.1 or Theorem 3.2). … References Bradley, Richard C. (2005), Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions. Probability Surveys 2, 107-144. doi: 10.1214/154957805100000104 …
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