Subgeometric ergodicity and β-mixing

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Abstract

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
Article numberarXiv:1904.07103
JournalarXiv.org
Number of pages15
ISSN2331-8422
Publication statusPublished - Apr 2019
MoE publication typeB1 Journal article

Fields of Science

  • 511 Economics
  • 112 Statistics and probability

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