Limiting behavior of random continued fractions
The main purpose of the paper is to investigate the probability for the \(\mu\)-random continued fraction \(K(a_{n}/b_{n})\), where \(\{(^{a_{n} } _{b_{n}})\}^{\infty}_{n=1}\) is a sequence of independent \(\mu\)-random variables from \(C^{2}_{0}\), to converge generally with probability 1 or to restrained with probability 1. The important step for the author is to apply four theorems proved by Furstenberg in 1963 (see [\textit{A. F. Beardon}, The geometry of discrete groups. Graduate Texts in Mathematics, 91. New York - Heidelberg - Berlin: Springer-Verlag (1983; Zbl 0528.30001)]).
scientific article; zbMATH DE number 6225227