Invariant densities for random continued fractions

Journal of Mathematical Analysis and Applications, vol. 512, pp. 126163

Abstract

We continue the study of random continued fraction expansions, generated by random application of the Gauss and the Rényi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous invariant measure with smooth density.

Authors 4

1. Charlene Kalle Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, the Netherlands

   Leiden University

2. Valentin Matache

   University of Nebraska at Omaha

   Affiliation as printed

   Department of Mathematics, University of Nebraska Omaha, USA

   University of Nebraska, . Omaha

3. Masato Tsujii

   Kyushu University

   Affiliation as printed

   Faculty of Mathematics, Kyushu University, Japan

   Kyushu University

4. Evgeny A. Verbitskiy corresponding Aachen Mathematical Institute

   Leiden University · University of Groningen

   Affiliation as printed

   Bernoulli Institute, Groningen University, the Netherlands

   Mathematical Institute, Leiden University, the Netherlands

   Leiden University