Subgeometric ergodicity and β-mixing

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It is well known that stationary geometrically ergodic Markov chains are β-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity impliesβ-mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies β-mixing with subgeometrically decaying mixing coefficients. Although this result is simple it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity can not be established. To illustrate our results we derive new subgeometric ergodicity and β-mixing results for the self-exciting threshold autoregressive model.
Original languageEnglish
JournalJournal of Applied Probability
Publication statusAccepted/In press - 2020
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 511 Economics
  • 112 Statistics and probability

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