2019
DOI: 10.1007/s10687-019-00346-2
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On maximum of Gaussian random field having unique maximum point of its variance

Abstract: Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using Double Sum Method under the widest possible conditions. R(s, t) = EX(s)X(t); denote by σ 2 (t) = R(t, t) its variance function, which is continuous since X is a.s. continuous. We study the asymptotic behavior of the probability P (S; u) = P(max t∈S X(t) >u)(1) as u → ∞. We nee… Show more

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Cited by 12 publications
(18 citation statements)
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“…From Conditions 3 and 4 it follows a regular variation property of r t (s). The following proposition is proved in [5].…”
Section: Condition 3 (Local Homogeneitymentioning
confidence: 94%
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“…From Conditions 3 and 4 it follows a regular variation property of r t (s). The following proposition is proved in [5].…”
Section: Condition 3 (Local Homogeneitymentioning
confidence: 94%
“…From this condition it follows V. A. Dmitrovsky's inequality, [1], [2], [10], which is more accurate than Borell-TIS one. Using this inequality, it is proved in [5] the following Lemma.…”
Section: General Settingmentioning
confidence: 99%
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