Random logistic maps. I
type: Item
instance of: scholarly article
title: Random logistic maps. I
zbMATH Open document ID: 0969.60069
DOI: 10.1023/A:1007828804691
published in: Journal of Theoretical Probability
publication date: 2001-09-23T00:00:00Z
review text: The paper studies iterations of i.i.d. random logistic maps, i.e. it studies the sequence \(X_{n+1}=C_{n+1}X_n(1-X_n)\) where \(C_n, n=1,2,\dots\), is a sequence of i.i.d. random variables with values in \([0,4].\) The authors show that \(X_n\) tends to zero a.s. if \(E\ln C_1<0\) and in probability if \(E\ln C_1=0\). If \(E\ln C_1>0\) and \(E|\ln(4-C_1)|<\infty\), then there exists an invariant measure of the corresponding Markov chain whose properties are discussed.
reviewed by: Yuri Kifer
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 1512533
zbMATH Keywords: random logistic maps
zbMATH Keywords: invariant measure
author: K. B. Athreya
author: Jack Jie Dai
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1512533