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Sampling local properties of attractors via Extreme Value Theory

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  • Faranda, Davide
  • Freitas, Jorge Milhazes
  • Guiraud, Pierre
  • Vaienti, Sandro

Abstract

We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed dynamical system. This will give information on the local geometrical properties of the stationary measure. We will consider systems perturbed with additive noise and with observational noise. Moreover we will apply our techniques to chaotic systems and to contractive systems, showing that both share the same qualitative behavior when perturbed.

Suggested Citation

  • Faranda, Davide & Freitas, Jorge Milhazes & Guiraud, Pierre & Vaienti, Sandro, 2015. "Sampling local properties of attractors via Extreme Value Theory," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 55-66.
    • Handle: RePEc:eee:chsofr:v:74:y:2015:i:c:p:55-66
    DOI: 10.1016/j.chaos.2015.01.016
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    References listed on IDEAS

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    1. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes, 2008. "On the link between dependence and independence in extreme value theory for dynamical systems," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1088-1093, July.
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