Abstract
Gaussian homogeneous fields on two-dimensional Euclidean space are considered, whose correlation functions behave at zero in a power-law manner along each of the coordinates. Exact asymptotics are evaluated for the exceedances probabilities above infinitely growing levels on lattices with different densities along each coordinate and with infinitely decreased lattice density. Relations between the evaluated asymptotic behavior and corresponding ones in continuous time at various rates of lattice densities are discussed.
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ACKNOWLEDGMENTS
The author thanks his scientific advisor V.I. Piterbarg for his attention to this work. The author also thanks the reviewer for his/her thorough reading of the paper and fruitful comments.
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Translated by E. Oborin
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Kozik, I.A. Extremes of Homogeneous Two-Parametric Gaussian Fields at Discretization of Parameters. Moscow Univ. Math. Bull. 77, 217–226 (2022). https://doi.org/10.3103/S0027132222050035
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DOI: https://doi.org/10.3103/S0027132222050035