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1 results

  • Excursion sets of three classes of stable random fields

  • Part of
  • Robert J. Adler, Gennady Samorodnitsky, Jonathan E. Taylor
  • Journal:
    Advances in Applied Probability / Volume 42 / Issue 2 / June 2010
    Published online by Cambridge University Press:
    01 July 2016, pp. 293-318
    Print publication:
    June 2010
    • Article
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  • Studying the geometry generated by Gaussian and Gaussian-related random fields via their excursion sets is now a well-developed and well-understood subject. The purely non-Gaussian scenario has, however, not been studied at all. In this paper we look at three classes of stable random fields, and obtain asymptotic formulae for the mean values of various geometric characteristics of their excursion sets over high levels. While the formulae are asymptotic, they contain enough information to show that not only do stable random fields exhibit geometric behaviour very different from that of Gaussian fields, but they also differ significantly among themselves.