Sharpness of the normal approximation of functionals of strongly correlated Gaussian random fields

DOI10.1007/BF01152556zbMath0716.60050MaRDI QIDQ753269

Nikolai N. Leonenko

Publication date: 1988

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

homogeneous isotropic Gaussian random fieldsstrongly correlated random fields

Mathematics Subject Classification ID

Random fields (60G60)

Related Items

Limit theorems for excursion sets of subordinated Gaussian random fields with long-range dependence ⋮ Limit Theorems for Excursion Sets of Stationary Random Fields ⋮ Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Central limit theorems for the excursion set volumes of weakly dependent random fields ⋮ Non-central limit theorems and convergence rates ⋮ On the rate of convergence to Rosenblatt-type distribution ⋮ Non-universal fluctuations of the empirical measure for isotropic stationary fields on \(\mathbb{S}^2\times \mathbb{R} \) ⋮ Exact parabolic asymptotics for singular \(n\)-D Burgers' random fields: Gaussian approximation ⋮ On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields ⋮ On rate of convergence in non-central limit theorems

Cites Work

• High level sojourns for strongly dependent Gaussian processes
• Some limit theorems for sojourn times of strongly dependent Gaussian processes
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Regularly varying functions
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