On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²

Marie Kratz () and Werner Nagel
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Marie Kratz: ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique
Werner Nagel: IENA - Institut fur Stochastik Ernst Friedrich-Schiller-Universitat Jena - FSU - Friedrich-Schiller-Universität Jena = Friedrich Schiller University Jena = Université de Iéna [Jena, Germany]

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Abstract: When a random field (Xt; t 2 R2) is thresholded on a given level u, the excursion set is given by its indicator 1[u;1)(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.

Keywords: Capacity functional; Stereology; Sweeping line method; Stochastic geometry; Second moment measure; Rice formulas; Crossings; Excursion set; Gaussian eld; Grow- ing circle method (search for similar items in EconPapers)
Date: 2014-10-29
Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01085072v1
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