College of Engineering >
Operations Research and Information Engineering >
ORIE Technical Reports >
Please use this identifier to cite or link to this item:
|Title: ||High level excursion set geometry for non-Gaussian infinitely divisible random fields|
|Authors: ||Adler, Robert|
|Keywords: ||infinitely divisible random fields|
|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
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|
Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.