Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence

DOI10.1080/07362994.2016.1230723zbMath1359.60066arXiv1501.02247OpenAlexW2963811485MaRDI QIDQ2968186

Murad S. Taqqu, Nikolai N. Leonenko, María D. Ruiz-Medina

Publication date: 10 March 2017

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

Full work available at URL: https://arxiv.org/abs/1501.02247

zbMATH Keywords

infinitely divisible distributionsHermite polynomialsFredholm determinantGaussian random fieldsRosenblatt distributionnon-central limit theoremsmultiple Wiener-Itô stochastic integrals

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Random fields (60G60) Gaussian processes (60G15) Characteristic functions; other transforms (60E10) Stochastic integrals (60H05) Limit theorems in probability theory (60F99)

Related Items (10)

Sojourn functionals for spatiotemporal Gaussian random fields with long memory ⋮ Limit theorems for filtered long-range dependent random fields ⋮ Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence ⋮ On some distributional properties of subordinated Gaussian random fields ⋮ Non-central limit theorems for functionals of random fields on hypersurfaces ⋮ Long range dependence of heavy-tailed random functions ⋮ Non-universal fluctuations of the empirical measure for isotropic stationary fields on \(\mathbb{S}^2\times \mathbb{R} \) ⋮ Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem ⋮ On rate of convergence in non-central limit theorems ⋮ Increasing domain asymptotics for the first Minkowski functional of spherical random fields

Cites Work

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• Properties and numerical evaluation of the Rosenblatt distribution
• On the distribution of the Rosenblatt process
• Sojourn measures of Student and Fisher-Snedecor random fields
• On the rate of convergence to Rosenblatt-type distribution
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples
• Noncentral limit theorems for quadratic forms in random variables having long-range dependence
• Unimodality of infinitely divisible distribution functions of class L
• Relative zeta functions, relative determinants and scattering theory
• Scattering theory and adiabatic decomposition of the \(\zeta\)-determinant of the Dirac Laplacian
• A note on Rosenblatt distributions
• Riesz potentials and Liouville operators on fractals
• Analytic and asymptotic properties of multivariate generalized Linnik's probability densities
• Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions
• Tauberian and Abelian theorems for long-range dependent random fields
• Two-sided eigenvalue estimates for subordinate processes in domains
• Fractals and Spectra
• ADIABATIC DECOMPOSITION OF THE -DETERMINANT OF THE DIRAC LAPLACIAN. I. THE CASE OF AN INVERTIBLE TANGENTIAL OPERATOR
• Mathematical Analysis of Evolution, Information, and Complexity
• An integral representation for selfdecomposable banach space valued random variables
• One cannot hear the shape of a drum
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables
• An extension of the notion of a generalized Γ-convolution
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Spectral properties of the operator of Riesz potential type
• Lévy Processes and Stochastic Calculus
• Random Fields and Geometry
• Regularly varying functions

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