Properties of invariant distributions and Lyapunov exponents for chaotic logistic maps
Hall, Peter A. & Wolff, Rodney C. (1995) Properties of invariant distributions and Lyapunov exponents for chaotic logistic maps. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 57(2), pp. 439-452.
Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling biological systems. We derive theory describing properties of the 'invariant' or 'stationary' distribution under logistic maps and apply those results in conjunction with numerical work to develop further properties of invariant distributions and Lyapunov exponents. We describe the role that poles play in determining properties of densities' iterated distributions and show how poles arise from iterated mappings of the centre of the interval to which the map is applied. Particular attention is paid to the shape of the invariant distribution in the tails or in the neighbourhood of a pole of its density. A new technique is developed for this application. it enables us to combine 'parametric' information, available from the structure of the map, with 'nonparametric' information obtainable from numerical experiments.
Citation countsare sourced monthly fromand citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
|Item Type:||Journal Article|
|Keywords:||Bandwidth, chaos, density estimation, invariant distribution, kernel method, logistic map, Lyapunov exponent, pole, stationary distribution|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100)|
Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > CLASSICAL PHYSICS (020300)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
|Divisions:||Current > QUT Faculties and Divisions > QUT Business School|
|Copyright Owner:||Copyright 1995 Blackwell Publishing|
|Copyright Statement:||Reproduced in accordance with the copyright policy of the publisher.|
|Deposited On:||19 Feb 2007|
|Last Modified:||05 Jan 2011 23:29|
Repository Staff Only: item control page