Central limit theorem for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields

DOI10.1007/s10959-017-0760-6zbMath1404.60034OpenAlexW2607203666MaRDI QIDQ1800954

Sreekar Vadlamani, Marie F. Kratz

Publication date: 26 October 2018

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-017-0760-6

zbMATH Keywords

chaos expansionGaussian fieldsexcursion setsLipschitz-Killing curvaturesCLT

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Integral geometry (53C65)

Related Items (14)

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 filtered long-range dependent random fields ⋮ On the excursion area of perturbed Gaussian fields ⋮ The phase transition for planar Gaussian percolation models without FKG ⋮ Reduction principle for functionals of vector random fields ⋮ On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields ⋮ Unnamed Item ⋮ 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 ⋮ Reduction principle for functionals of strong-weak dependent vector random fields ⋮ Testing marginal symmetry of digital noise images through the perimeter of excursion sets ⋮ The effect of discretization on the mean geometry of a 2D random field

Cites Work

• Unnamed Item
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• High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere
• Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds
• A central limit theorem for the Euler characteristic of a Gaussian excursion set
• Functional central limit theorem for the volume of excursion sets generated by associated random fields
• Quantitative Breuer-Major theorems
• On the second moment of the number of crossings by a stationary Gaussian process
• Multiple Wiener-Itô integral expansions for level-crossing-count functionals
• Level crossings and other level functionals of stationary Gaussian processes
• MWI representation of the number of curve-crossings by a differentiable Gaussian process, with applications
• Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes
• A quantitative central limit theorem for the Euler-Poincaré characteristic of random spherical eigenfunctions
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• A central limit theorem for the Euler integral of a Gaussian random field
• On the rate of convergence for central limit theorems of sojourn times of Gaussian fields
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• Level Sets and Extrema of Random Processes and Fields
• CLT and other limit theorems for functionals of Gaussian processes
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• Random Fields and Geometry
• On the Variance of the Number of Zeros of a Stationary Gaussian Process
• Tubes and Spheres in n-Spaces, and a Class of Statistical Problems
• On the Volume of Tubes
• Central limit theorems for the number of maxima and an estimator of the second spectral moment of a stationary Gaussian process, with application to hydroscience
• Central limit theorems for level functionals of stationary Gaussian processes and fields

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