Large deviations in expanding random dynamical systems
type: Item
instance of: scholarly article
title: Large deviations in expanding random dynamical systems
zbMATH Open document ID: 0959.60021
author: Thomas Bogenschütz
author: Achim Doebler
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors prove large deviations results for random dynamical systems [see also \textit{Y. Kifer}, in: Lyapunov exponents. Lect. Notes Math. 1486, 178-186 (1991; Zbl 0744.58061)]. Large deviations results in ergodic theory deal with occupational measures \(\mu_{x}^{n}=\frac{1}{n}\sum_{i=0}^{n-1}\delta_{\varphi^{i} x}\) on a topological dynamical system \((X,{\mathcal B},\mu,\varphi)\). Here \(X\) is a compact metric space, \({\mathcal B}\) is the Borel-\(\sigma\)-algebra on \(X\), \(\mu\) is a probability on \((X,{\mathcal B})\) and \(\varphi\) is a \(\mu\)-preserving continuous transformation on \(X\), the set of probability measures being topologized by weak convergence. For random dynamical systems the iteration of one single transformation is replaced by the successive application of randomly chosen transformations [see the thermodynamic formalism of \textit{T. Bogenschütz}, Random Comput. Dyn. 1, No. 1, 99-116 (1993; Zbl 0848.28010)]. In Kifer's work the results are concerned with occupational measures of the skew-product transformation induced by the random dynamical system. In the present paper the authors give a uniform rate function for large deviations for occupational measures of the corresponding cocycle.
reviewed by: Mihai Gradinaru
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37H99
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 1492606
zbMATH Keywords: large deviations
zbMATH Keywords: random dynamical systems
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.805
OpenAlex ID: W2079957470
DOI: 10.3934/DCDS.1999.5.805
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description: scientific article; zbMATH DE number 1492606