Random iteration of one-dimensional transformations
type: Item
instance of: scholarly article
title: Random iteration of one-dimensional transformations
zbMATH Open document ID: 0583.60061
author: Takehiko Morita
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let S be a measurable space, \(\{f_ s\}_{s\in S}\) a family of transformations from the unit interval into itself, and \(\{X_ n\}^{\infty}_{n=1}\) a sequence of S-valued i.i.d. random variables on a probability space \((\Omega,{\mathcal F},P)\). The author studies the asymptotic behavior of \(x_ n\) where \(x_{n+1}=f_{X_{n+1}(\omega)}(x_ n)\), \(n\geq 0\), \(\omega\in \Omega\). The results generalize those of \textit{S. Tanaka} and \textit{S. Itô} [Tokyo J. Math. 5, 463-478 (1984; Zbl 0528.60065)].
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 3934146
zbMATH Keywords: transformations from the unit interval into itself
zbMATH Keywords: asymptotic behavior
reviewed by: Kenneth S. Miller
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3934146