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

Fetima Ladjimi and Marc Peigné

Statistics & Probability Letters, 2019, vol. 145, issue C, 1-11

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.

Keywords: Iterated function systems; Quasi-compact linear operators; Invariant probability measure; Absorbing compact set (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.05.019

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