September 2016 On the capacity functional of excursion sets of Gaussian random fields on ℝ2
Marie Kratz, Werner Nagel
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Adv. in Appl. Probab. 48(3): 712-725 (September 2016).

Abstract

When a random field (Xt,t∈ℝ2) is thresholded on a given level u, the excursion set is given by its indicator 1[u, ∞)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets as, e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular, Rice methods, and from integral and stochastic geometry.

Citation

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Marie Kratz. Werner Nagel. "On the capacity functional of excursion sets of Gaussian random fields on ℝ2." Adv. in Appl. Probab. 48 (3) 712 - 725, September 2016.

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 1351.60063
MathSciNet: MR3568888

Subjects:
Primary: 60G15
Secondary: 60D05 , 60G60

Keywords: Capacity functional , crossings , excursion set , Gaussian field , growing circle method , Rice formula , second moment measure , stereology , Stochastic geometry , sweeping line method

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 3 • September 2016
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