IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/99cf54.html
   My bibliography  Save this paper

Maximum of Gaussian Field on Piecewise Smooth Domain: Equivalence of Tube Method and Euler Characteristic Method

Author

Listed:
  • Akimichi Takemura

    (Faculty of Economics, University of Tokyo.)

  • Satoshi Kuriki

    (The Institute of Statistical Mathematics)

Abstract

Consider a Gaussian random field Z(u) with mean 0, variance 1, and finite Karhunen-Loeve expansion. Under a very general assumption that the index set M is a manifold with piecewise smooth boundary, we prove the validity and the equivalence of two currently available methods for obtaining the asymptotic expansion of tail probability of the maximum of Z(u). One is the tube method, where the volume of tube around the index set M is evaluated. The other is the Euler characteristic method, where the expectation for the Euler characteristic of excursion set is evaluated. In order to show this equivalence we prove a version of the Morse's theorem for a manifold with piecewise smooth boundary. These results on the tail probabilities are generalizations of those of Takemura and Kuriki (1997), where M was assumed to be convex.

Suggested Citation

  • Akimichi Takemura & Satoshi Kuriki, 1999. "Maximum of Gaussian Field on Piecewise Smooth Domain: Equivalence of Tube Method and Euler Characteristic Method," CIRJE F-Series CIRJE-F-54, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:99cf54
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/99/cf54/contents.htm
    Download Restriction: no

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tky:fseres:99cf54. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office). General contact details of provider: http://edirc.repec.org/data/ritokjp.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.