Iterated function systems with place dependent probabilities and application to the Diaconis-Friedman's chain on [0, 1]

Système d'itération de transformations aléatoires avec des transition en dépendance spatiale. Application à la chaîne de Diaconis-Friedman

Fetima Ladjimi (1) , Marc Peigné (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study Markov chains generated by iterated Lipschitz functions systems with possibly place dependent probabilities. Under general conditions, we prove uniqueness of the invariant probability measure for the associated Markov chain, by using quasi-compact linear operators technics. We use the same approach to describe the behavior of the Diaconis-Friedman's chain on [0, 1] with possibly place dependent probabilities.

Mots clés: AMS classification: 60J05; 60F05; Iterated function systems; quasi-compact linear operators; invariant probability measure; absorbing compact set

Domaines: Probabilités [math.PR]

Fetima Ladjimi, Marc Peigné. Iterated function systems with place dependent probabilities and application to the Diaconis-Friedman's chain on [0, 1]. Statistics and Probability Letters, 2019. ⟨hal-01567392⟩