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

被引：0

作者：

Gabriela Ileana Sebe

机构：

[1] University Politehnica of Bucharest,

[2] Romania,undefined

来源：

Monatshefte für Mathematik | 2001年 / 133卷

关键词：

2000 Mathematics Subject Classification: 28D05; 11K55; Key words: Ergodicity; grotesque continued fractions; infinite-order-chain; random system with complete connections;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：241 / 254

页数：13

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