Limiting behavior of random continued fractions
type: Item
instance of: scholarly article
title: Limiting behavior of random continued fractions
zbMATH Open document ID: 1300.40001
author: Lisa Lorentzen
published in: Constructive Approximation
publication date: 2013-11-11T00:00:00Z
review text: 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)]).
reviewed by: Chrysoula G. Kokologiannaki
Mathematics Subject Classification ID: 40A15
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 6225227
zbMATH Keywords: iterated function systems
zbMATH Keywords: random Möbius transformations
zbMATH Keywords: linear fractional transformations
zbMATH Keywords: general convergence
zbMATH Keywords: restrained sequences
zbMATH Keywords: random composition sequences
zbMATH Keywords: random continued factions
zbMATH Keywords: Furstenberg's theorem
MaRDI profile type: Publication
full work available at URL: s00365-013-9198-y
OpenAlex ID: W2148494773
cites work: Random iteration of Möbius transformations and Furstenberg's theorem
cites work: Q3310101
cites work: Noncommuting Random Products
cites work: General Convergence of Continued Fractions
cites work: Limiting Structures for Sequences of Linear Fractional Transformations
cites work: Continued fractions. Vol. 1: Convergence theory
DOI: 10.1007/S00365-013-9198-Y
description: scientific article; zbMATH DE number 6225227