Asymptotic behaviour of level sets of needlet random fields

DOI10.1016/j.spa.2022.10.011OpenAlexW3094797755MaRDI QIDQ2105072

Radomyra Shevchenko, Anna Paola Todino

Publication date: 8 December 2022

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

Full work available at URL: https://arxiv.org/abs/2011.02856

zbMATH Keywords

central limit theoremWiener chaosexcursion setsboundary lengthGaussian spherical eigenfunctionsspherical needlets

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Inference from stochastic processes and spectral analysis (62M15) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Spherical harmonics (33C55)

Related Items (4)

Nonparametric needlet estimation for partial derivatives of a probability density function on the d -torus ⋮ On the relation between Fourier and Walsh-Rademacher spectra for random fields ⋮ Flexible-bandwidth needlets ⋮ No smooth phase transition for the nodal length of band-limited spherical random fields

Cites Work

• Unnamed Item
• High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere
• Concentration inequalities and confidence bands for needlet density estimators on compact homogeneous manifolds
• On the limiting behaviour of needlets polyspectra
• Needlet approximation for isotropic random fields on the sphere
• Fluctuations of the nodal length of random spherical harmonics
• On the dependence structure of wavelet coefficients for spherical random fields
• Mean-square continuity on homogeneous spaces of compact groups
• Decomposition of Besov and Triebel-Lizorkin spaces on the sphere
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Practical wavelet design on the sphere
• Asymptotics for spherical needlets
• Adaptive density estimation for directional data using needlets
• Asymptotic uncorrelation for Mexican needlets
• Central limit theorems for non-linear functionals of Gaussian fields
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Nonparametric regression using needlet kernels for spherical data
• Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors
• Invariant random fields in vector bundles and application to cosmology
• The needlets bispectrum
• The asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonics
• Asymptotic expansion of Legendre polynomials with respect to the index near \(x = 1\): generalization of the Mehler-Rayleigh formula
• On the correlation between nodal and nonzero level sets for random spherical harmonics
• Normal approximations for wavelet coefficients on spherical Poisson fields
• Phase singularities in complex arithmetic random waves
• Cosmological applications of a wavelet analysis on the sphere
• Continuous wavelets on compact manifolds
• A central limit theorem for Lipschitz-Killing curvatures of Gaussian excursions
• Fully discrete needlet approximation on the sphere
• Localisation of directional scale-discretised wavelets on the sphere
• Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
• On the area of excursion sets of spherical Gaussian eigenfunctions
• Normal Approximations with Malliavin Calculus
• Random Fields on the Sphere
• Random nodal lengths and Wiener chaos
• The Malliavin Calculus and Related Topics
• Localized Tight Frames on Spheres
• On the distribution of the nodal sets of random spherical harmonics
• Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos
• Random Fields and Geometry
• Sparse Image and Signal Processing
• Central limit theorems for level functionals of stationary Gaussian processes and fields

This page was built for publication: Asymptotic behaviour of level sets of needlet random fields