IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v74y2015icp55-66.html
   My bibliography  Save this article

Sampling local properties of attractors via Extreme Value Theory

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915000235
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.01.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Livieri, Giulia & Lillo, Fabrizio & Marmi, Stefano & Solomko, Anton & Vaienti, Sandro, 2023. "Unimodal maps perturbed by heteroscedastic noise: an application to a financial systems," LSE Research Online Documents on Economics 120290, London School of Economics and Political Science, LSE Library.
    2. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike & Vaienti, Sandro, 2016. "Rare events for the Manneville–Pomeau map," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3463-3479.
    3. Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes & Todd, Mike, 2015. "Speed of convergence for laws of rare events and escape rates," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1653-1687.
    4. Freitas, Ana Cristina Moreira, 2009. "Statistics of the maximum for the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 604-608.
    5. Angel, Omer & Matzavinos, Anastasios & Roitershtein, Alexander, 2019. "Limit theorem for the Robin Hood game," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 9-15.
    6. George Haiman, 2018. "Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 553-562, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:74:y:2015:i:c:p:55-66. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.