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• W2055084071 abstract "Abstract We discuss a counter-example to the traditional view that stochastic processes lead to a non-convergence of the correlation dimension in computed or measured time series. Specifically we show that a simple class of “colored” random noises characterized by a power-law power spectrum have a finite and predictable value for the correlation dimension. These results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics. We demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties. The consequent exploitation of the non-Gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis. We apply this approach to characterize several “global” properties of random noise." @default.
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• W2055084071 date "1989-05-01" @default.
• W2055084071 modified "2023-10-17" @default.
• W2055084071 title "Finite correlation dimension for stochastic systems with power-law spectra" @default.
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• W2055084071 doi "https://doi.org/10.1016/0167-2789(89)90075-4" @default.
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