A central limit theorem for Lipschitz-Killing curvatures of Gaussian excursions

DOI10.1016/j.jmaa.2017.03.036zbMath1373.60054arXiv1607.06696OpenAlexW2484774344MaRDI QIDQ2396678

Dennis Müller

Publication date: 24 May 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06696

zbMATH Keywords

central limit theoremGaussian random fieldWiener chaos expansionexcursion setLipschitz-Killing curvatureMalliavin-Stein method

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (9)

Fluctuations of the number of excursion sets of planar Gaussian fields ⋮ On 3-dimensional Berry's model ⋮ Characterization of anisotropic Gaussian random fields by Minkowski tensors ⋮ Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence ⋮ On the excursion area of perturbed Gaussian fields ⋮ On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields ⋮ Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields ⋮ Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images ⋮ Asymptotic behaviour of level sets of needlet random fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Second-order properties and central limit theorems for geometric functionals of Boolean models
• Number of critical points of a Gaussian random field: condition for a finite variance
• A central limit theorem for the Euler characteristic of a Gaussian excursion set
• Multiple Wiener-Itô integral expansions for level-crossing-count functionals
• Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
• Chaos expansions of double intersection local time of Brownian motion in \(\mathbb{R}^ d\) and renormalization
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• On the existence of paths between points in high level excursion sets of Gaussian random fields
• Phase singularities in isotropic random waves
• Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
• Normal Approximations with Malliavin Calculus
• Limit Theorems for Excursion Sets of Stationary Random Fields
• Stochastic and Integral Geometry
• Level Sets and Extrema of Random Processes and Fields
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• Gaussian Hilbert Spaces
• Second Order Analysis of Geometric Functionals of Boolean Models
• Central limit theorems for level functionals of stationary Gaussian processes and fields

This page was built for publication: A central limit theorem for Lipschitz-Killing curvatures of Gaussian excursions