A Gauss-Kuzmin theorem for the Rosen fractions (Q558141)

Using the natural extensions for the Rosen maps, the author gives an infinite order-chain representation of the sequence of incomplete quotients of the Rosen fractions. She shows that the random systems with complete connections associated with the Rosen continued fraction expansion are with contraction and their transition operators are regular with respect to the Banach space of Lipschitz functions. This leads to a solution of a version of the Gauss-Kuzmin problem for the Rosen fractions.