Consistent Lyapunov exponent estimation for one-dimensional dynamical systems
type: Item
instance of: scholarly article
title: Consistent Lyapunov exponent estimation for one-dimensional dynamical systems
zbMATH Open document ID: 1066.37048
DOI: 10.1007/BF02892054
author: Salim Lardjane
published in: Computational Statistics
publication date: 2005-05-20T00:00:00Z
review text: Consider a sample \(x_0,\dots,x_T\) from a trajectory \((x_t)_{t\in \mathbb N}\) of the dynamical system \(([0,1], B, S,\mu)\), where \(B\) is the completion of the Borel \(\sigma\)-algebra of \([0,1]\) with respect to probabilistic measure \(\mu\), and let \( S [0,1]\rightarrow [0,1]\) be a measurable map such that the Lyapunov exponent \(\lambda=\int_{[0,1]} \log | S^{'}| d\mu\) is well defined. The author considers the problem of estimating \(\lambda\) for the unknown map \(S\) using the observed sample \(x_0,\dots,x_T\). He proves the consistency of a nearest neighbour estimator of the Lyapunov exponent for a rather general class of one-dimensional ergodic dynamical systems and demonstrates that this estimator has good practical properties via a simulation experiment.
Mathematics Subject Classification ID: 37M25
Mathematics Subject Classification ID: 37E05
zbMATH DE Number: 2169403
zbMATH Keywords: chaos
zbMATH Keywords: ergodicity
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: nearest neighbours estimation
zbMATH Keywords: consistency
MaRDI profile type: Publication
cites work: Q4357052
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full work available at URL: https://doi.org/10.1007/bf02892054
OpenAlex ID: W1971664617
description: scientific article; zbMATH DE number 2169403