A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian\n Excursions

2016/07/22 by Dennis Müller, Müller, Dennis · 1 citation
Agricultural and Biological Sciences · Economics, Econometrics and Finance · Mathematics · #60D05 #60F05 (Primary) #60G15 (Secondary) #60G60 #FOS: Mathematics #Financial Risk and Volatility Modeling #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR) #Soil erosion and sediment transport

paper · pdf · doi:10.48550/arxiv.1607.06696

openalex publication_date 2016/07/22 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

This paper studies the excursion set of a real stationary isotropic Gaussian\nrandom field above a fixed level. We show that the standardized\nLipschitz-Killing curvatures of the intersection of the excursion set with a\nwindow converges in distribution to a normal distribution as the window grows\nto the d-dimensional Euclidean space. Moreover a lower bound for the\nasymptotic variance is shown.\n

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