On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

DOI10.1016/j.spa.2013.01.016zbMath1302.60050arXiv1303.2495OpenAlexW2023094713MaRDI QIDQ2444636

Viet-Hung Pham

Publication date: 10 April 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2495

zbMATH Keywords

Malliavin calculusHermite polynomialssojourn timeGaussian field

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (11)

Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence ⋮ Kolmogorov distance for the central limit theorems of the Wiener chaos expansion and applications ⋮ Quantitative central limit theorems of spherical sojourn times of isotropic Gaussian fields ⋮ On the excursion area of perturbed Gaussian fields ⋮ Kernel representation formula: from complex to real Wiener-Itô integrals and vice versa ⋮ Approximate normality of high-energy hyperspherical eigenfunctions ⋮ On the limiting behaviour of needlets polyspectra ⋮ Central limit theorem for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields ⋮ On rate of convergence in non-central limit theorems ⋮ The defect of random hyperspherical harmonics ⋮ Increasing domain asymptotics for the first Minkowski functional of spherical random fields

Cites Work

• Central limit theorems for the excursion set volumes of weakly dependent random fields
• Quantitative Breuer-Major theorems
• Central limit theorems and quadratic variations in terms of spectral density
• Stein's method on Wiener chaos
• Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• Central limit theorems for sequences of multiple stochastic integrals
• CLT and other limit theorems for functionals of Gaussian processes
• Limit theorems for non-linear functionals of Gaussian sequences
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