A Functional Limit Theorem for the Integrals over Level Sets of a Gaussian Random Field

DOI10.1137/S0040585X97T987557zbMath1334.60046OpenAlexW2293913094MaRDI QIDQ2790687

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Publication date: 8 March 2016

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t987557

zbMATH Keywords

functional central limit theoremHausdorff measurelocal timelevel setscoarea formulaGaussian random fields

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Random measures (60G57) Functional limit theorems; invariance principles (60F17)

Cites Work

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• Level crossings and other level functionals of stationary Gaussian processes
• Crossings of smooth shot noise processes
• A functional central limit theorem for the level measure of a Gaussian random field
• On random surface area
• Level Sets and Extrema of Random Processes and Fields
• Random Fields and Geometry
• Functional Central Limit Theorem for the Measures of Level Surfaces of the Gaussian Random Field
• Local Times and Sample Function Properties of Stationary Gaussian Processes
• Normal approximation for quasi-associated random fields

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