Consistent Estimation of a Dynamical Map

Andrew Nobel

Chapter Chapter 11 in Nonlinear Dynamics and Statistics, 2001, pp 267-280 from Springer

Abstract: Abstract Estimation of a nonlinear map F governing the evolution of an observed dynamical system is considered in two specific models. In the first model, F is successively applied to a fixed initial vector in the absence of noise, so that the the observed states of the system constitute a trajectory of F. In the second, dynamical noise model, the system is perturbed by independent noise between each application of F. Estimates of F are proposed for each model, and are shown to be consistent under general conditions. No assumptions are made regarding mixing rates of the observations. Both continuous and general measurable maps F are considered.

Keywords: Lyapunov Exponent; Springer Lecture Note; Chaotic Time Series; Random Dynamical System; Finite Partition (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0177-9_11

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DOI: 10.1007/978-1-4612-0177-9_11

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