Excursion sets of stable random fields

Details Excursion sets of stable random fields Excursion sets of stable random fields

2007-12-27

arxiv.org/abs/0712.4276v1

Mathematics

Probability

35 pages, 1 figure

Scientific paper

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.

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