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On Convergence Rate in the Gauss–Kuzmin Problem for Grotesque Continued Fractions

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Abstract.

 We give an infinite-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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  1. University Politehnica of Bucharest, Romania, , , , , , RO

    Gabriela Ileana Sebe

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  1. Gabriela Ileana Sebe
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(Received 9 October 2000; in revised form 27 March 2001)

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Sebe, G. On Convergence Rate in the Gauss–Kuzmin Problem for Grotesque Continued Fractions. Mh Math 133, 241–254 (2001). https://doi.org/10.1007/s006050170022

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  • DOI: https://doi.org/10.1007/s006050170022

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