CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields

Marie Kratz () and Sreekar Vadlamani
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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
Sreekar Vadlamani: TIFR-CAM - Center for Applicable Mathematics [Bangalore] - TIFR - Tata Institute for Fundamental Research

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Abstract: Our interest in this paper is to explore limit theorems for various geometric function-als of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times (see [4, 13, 14, 18, 22, 25] for a sample of works in such settings). The most recent addition being [6] where a central limit theorem (CLT) for Euler-Poincaré characteristic of the excursions set of a Gaussian random field is proven under appropriate conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz-Killing curvatures of excursion sets of Gaussian random fields in an appropriate setting.

Keywords: excursion sets; Lipschitz-Killing curvatures; chaos expansion; Gaussian fields; CLT (search for similar items in EconPapers)
Date: 2016-08
New Economics Papers: this item is included in nep-ecm
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