A dependence with complete connections approach to generalized Rényi continued fractions
arXiv:1810.10246
Abstract
We introduce and study in detail a special class of backward continued fractions that represents a generalization of Rényi continued fractions. We investigate the main metrical properties of the digits occurring in these expansions and we construct the natural extension for the transformation that generates the Rényi-type expansion. Also we define the associated random system with complete connections whose ergodic behavior allows us to prove a variant of Gauss-Kuzmin-type theorem.
18 pages