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On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]

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  • Ladjimi, Fetima
  • Peigné, Marc

Abstract

We describe the asymptotic behavior of the Diaconis–Freedman chain on [0,1], using technics developed to study iterated Lipschitz functions systems with possibly place dependent probabilities. Under some general conditions on this family of probabilities and using quasi-compact linear operators technics, we obtain a necessary and sufficient condition for the uniqueness of the stationary probability measure for this chain and explore the case when it does not hold.

Suggested Citation

  • Ladjimi, Fetima & Peigné, Marc, 2019. "On the asymptotic behavior of the Diaconis–Freedman chain on [0,1]," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 1-11.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:1-11
    DOI: 10.1016/j.spl.2018.05.019
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    References listed on IDEAS

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    1. Stoyanov, Jordan & Pirinsky, Christo, 2000. "Random motions, classes of ergodic Markov chains and beta distributions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 293-304, November.
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