Locally contractive iterated function systems
type: Item
instance of: scholarly article
title: Locally contractive iterated function systems
zbMATH Open document ID: 0974.37037
author: David Steinsaltz
published in: The Annals of Probability
publication date: 2000-08-27T00:00:00Z
review text: An iterated function system on \(X\subset \mathbb{R}^d\) is defined by successively applying and i.i.d. sequence of random Lipschitz functions from \(X\) to \(X\). This paper shows how \(F_n=f_1 \circ\cdots \circ f_n\) may converge even in the absence of the strong contraction conditions, for instance, Lipschitz constant smaller than 1 on average, which earlier work has required. Instead, it is required that there be a region of contraction which compensates for the noncontractive or even expansive part of the functions. Applications to queues, to self-modifying random walks and random logistic maps are given.
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 26A18
zbMATH DE Number: 1496115
zbMATH Keywords: iterated function system
zbMATH Keywords: random walk
zbMATH Keywords: randomness
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022677556
OpenAlex ID: W4245427736
DOI: 10.1214/AOP/1022677556
description: scientific article; zbMATH DE number 1496115