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Extracting Dynamical Behavior via Markov Models

In: Nonlinear Dynamics and Statistics

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  • Gary Froyland

Abstract

Statistical properties of chaotic dynamical systems are difficult to estimate reliably. Using long trajectories as data sets sometimes produces misleading results. It has been recognized for some time that statistical properties are often stable under the addition of a small amount of noise. Rather than analyzing the dynamical system directly, we slightly perturb it to create a Markov model. The analogous statistical properties of the Markov model often have “closed forms” and are easily computed numerically. The Markov construction is observed to provide extremely robust estimates and has the theoretical advantage of allowing one to prove convergence in the noise → 0 limit and produce rigorous error bounds for statistical quantities. We review the latest results and techniques in this area.

Suggested Citation

  • Gary Froyland, 2001. "Extracting Dynamical Behavior via Markov Models," Springer Books, in: Alistair I. Mees (ed.), Nonlinear Dynamics and Statistics, chapter 0, pages 281-321, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0177-9_12
    DOI: 10.1007/978-1-4612-0177-9_12
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