Random perturbations of transformations of an interval
type: Item
instance of: scholarly article
title: Random perturbations of transformations of an interval
zbMATH Open document ID: 0616.60064
DOI: 10.1007/BF02792539
author: Anatole Katok
author: Yuri Kifer
published in: Journal d'Analyse Mathématique
publication date: 1986-01-01T00:00:00Z
review text: The main result is as follows: Consider a map f of the interval [0,1] which is ergodic with invariant measure \(\mu_ f\), and a Markov chain \(x_ n^{\epsilon}\) with invariant measure \(\mu^{\epsilon}\) which is a small random perturbation of f. Then \(\mu^{\epsilon}\) converges weakly to \(\mu_ f\) as \(\epsilon\to 0\).
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 3998911
zbMATH Keywords: stability
zbMATH Keywords: invariant measure
zbMATH Keywords: small random perturbation
MaRDI profile type: Publication
cites work: Randomness implies order
cites work: Q3908199
cites work: Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
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cites work: Absolutely continuous measures for certain maps of an interval
cites work: Q4085018
full work available at URL: https://doi.org/10.1007/bf02792539
OpenAlex ID: W2078453944
description: scientific article; zbMATH DE number 3998911