Even the first iterate of a Markov operator is contracting in an \(L_ 2\) norm
type: Item
instance of: scholarly article
title: Even the first iterate of a Markov operator is contracting in an \(L_ 2\) norm
zbMATH Open document ID: 0833.60097
DOI: 10.1007/BF02188579
author: S. V. Ershov
published in: Journal of Statistical Physics
publication date: 1995-09-11T00:00:00Z
review text: The author investigates the relaxation toward the statistical equilibrium in the noisy maps \(x_{n+1} = f(x_n) + \zeta_n\), where \(\zeta\) is a random noise with distribution \(w(\zeta)\). A weighted \(L_2\) norm is introduced in which Markov operators (associated with noisy maps) are contracting provided the kernel is smooth enough. The significance of such norms for spatiotemporal chaos and random fields is discussed.
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 795353
zbMATH Keywords: Markov operators
zbMATH Keywords: noisy map
zbMATH Keywords: attractors
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Macrodynamics: Large-scale structures in turbulent media
cites work: The influence of noise on the logistic model
cites work: Asymptotic Periodicity of the Iterates of Markov Operators
cites work: Ergodic theory of chaos and strange attractors
cites work: Ergodic properties of invariant measures for piecewise monotonic transformations
full work available at URL: https://doi.org/10.1007/bf02188579
OpenAlex ID: W1969347824
description: scientific article; zbMATH DE number 795353