On the $\psi$-mixing coefficients of R\'enyi-type maps

TL;DR

This paper studies the dependence properties of sequences derived from Rényi-type continued fractions using dependence with complete connections and Lévy-type methods to establish bounds on their $oldsymbol{\psi}$-mixing coefficients.

Contribution

It introduces new bounds for the $oldsymbol{\psi}$-mixing coefficients of sequences from Rényi-type continued fractions using dependence with complete connections and Lévy-type techniques.

Findings

Established upper bounds for $oldsymbol{\psi}$-mixing coefficients.

Analyzed both incomplete and extended incomplete quotient sequences.

Applied Lévy-type approach for dependence estimation.

Abstract

Via dependence with complete connections we investigate the $\psi$-mixing coefficients of the sequence $(a_n)_{n \in \mathbb{N}}$ of incomplete quotients and also of the doubly infinite sequence $(\overline{a}_l)_{l \in \mathbb{Z}}$ of extended incomplete quotients of the R\'enyi-type continued fraction expansions. A L\'evy-type approach allows us to obtain good upper bounds for these coefficients.