IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01085072.html
   My bibliography  Save this paper

On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²

Author

Listed:
  • Marie Kratz

    (ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique)

  • Werner Nagel

    (IENA - Institut fur Stochastik Ernst Friedrich-Schiller-Universitat Jena - Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany])

Abstract

When a random field (Xt; t 2 R2) is thresholded on a given level u, the excursion set is given by its indicator 1[u;1)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry.

Suggested Citation

  • Marie Kratz & Werner Nagel, 2014. "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²," Working Papers hal-01085072, HAL.
    • Handle: RePEc:hal:wpaper:hal-01085072
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01085072
    as

    Download full text from publisher

    File URL: https://essec.hal.science/hal-01085072/document
    Download Restriction: no
    ---><---

    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:hal:wpaper:hal-01085072. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.