Sharpness of the normal approximation of functionals of strongly correlated Gaussian random fields
type: Item
instance of: scholarly article
title: Sharpness of the normal approximation of functionals of strongly correlated Gaussian random fields
zbMATH Open document ID: 0716.60050
DOI: 10.1007/BF01152556
author: Nikolai N. Leonenko
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: We consider estimates for the rate of convergence to the normal law of appropriately normalized and centralized integral-type functionals of homogeneous isotropic Gaussian random fields. We consider strongly correlated random fields, i.e., those for which the integral of the correlation function of the field diverges. We apply the direct probability method, arising in [\textit{V. V. Petrov}, Trudy vsesojuzn. Sovešč. Teor. Verojatn. mat. Statist., Erevan 1958, 38-44 (1960; Zbl 0100.345)]. As special cases, we consider geometric-type functionals of a Gaussian field, such as ``level set'', ``random volume'', ``random cross-sectional area'', etc. Such functionals arise in concrete applied problems.
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 4180437
zbMATH Keywords: homogeneous isotropic Gaussian random fields
zbMATH Keywords: strongly correlated random fields
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4180437