Estimating Invariant Probability Densities for Dynamical Systems

Authors: Kilminster D.¹; Allingham D.¹; Mees A.²

Source: Annals of the Institute of Statistical Mathematics, Volume 54, Number 1, 2002 , pp. 224-233(10)

Publisher: Springer

Buy & download fulltext article:

The full text article is not available.

At present, only title information is available on ingentaconnect.com for this article. This is due to copyright restrictions.

Abstract:

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.

Keywords: Nonlinear dynamics; probability density; invariant measure; Radon transform

Language: English

Document Type: Research article

Affiliations: 1: Centre for Applied Dynamics and Optimization, The University of Western Australia, 35 Stirling Highway, Nedlands, WA 6009, Australia 2: Centre for Applied Dynamics and Optimization, The University of Western Australia, 35 Stirling Highway, Nedlands, WA 6009, Australia; Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, H

Publication date: 2002-01-01