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Title: High level excursion set geometry for non-Gaussian infinitely divisible random fields
Authors: Adler, Robert
Samorodnitsky, Gennady
Taylor, Jonathan
Keywords: infinitely divisible random fields
moving average
excursion sets
critical points
Euler characteristic
Morse theory
Issue Date: 4-Aug-2009
Abstract: We consider smooth, infinitely divisible random fields with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets over high levels u. For a large class of such random fields we compute the asymptotic joint distribution of the numbers of critical points, of various types, of the random field in the excursion set, conditional on the latter being non-empty. This allows us, for example, to obtain the asymptotic conditional distribution of the Euler characteristic of the excursion set. In a significant departure from the Gaussian situation, the high level excursion sets for these random fields can have quite a complicated geometry. Whereas in the Gaussian case non-empty excursion sets are, with high probability, roughly ellipsoidal, in the more general infinitely divisible setting almost any shape is possible.
Appears in Collections:ORIE Technical Reports

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