 Properties of distributions and correlation integrals for generalised versions of the logistic mapPeter Hall and Rodney Carl Wolff Stochastic Processes and their Applications, 1998, vol. 77, issue 1, 123-137 Abstract: We study a generalised version of the logistic map of the unit interval in which the point is taken to . Here, is a parameter of the map, which has received attention only when and . We obtain the invariant density when , and derive properties of invariant distributions in all other cases. These are obtained by a mixture of analytic and numerical argument. In particular, we develop a technique for combining "parametric" information, available from the functional form of the map, with "non-parametric" information, from a Monte Carlo study. Properties of the correlation integral under the invariant distribution are also derived. It is shown that classical behaviour of this test statistic, which demands that the logarithm of the integral have slope equal to the lag, is valid if and only if . Keywords: Chaos; Correlation; integral; Invariant; distribution; Logistic; map (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:77:y:1998:i:1:p:123-137 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.