On Convergence Rate in the Gauss-Kuzmin Problem for Grotesque Continued Fractions (original) (raw)

Abstract

We give an in®nite-order-chain representation of the sequence of the incomplete quotients of the grotesque continued fraction expansion. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to prove a Gauss± Kuzmin-type theorem for this expansion. Finally, we derive a two-dimensional Gauss±Kuzmin theorem and also obtain an estimate of the convergence rate.

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