Sharpness of the normal approximation of functionals of strongly correlated Gaussian random fields
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.
homogeneous isotropic Gaussian random fields
scientific article; zbMATH DE number 4180437
scientific article