On the $\psi$-mixing coefficients of Rényi-type maps

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 Rényi-type continued fraction expansions. A Lévy-type approach allows us to obtain good upper bounds for these coefficients.