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K. Debicki et al., « Extremes of homogeneous Gaussian random fields », Serveur académique Lausannois, ID : 10670/1.53h1dy
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Let {X (s, t): s, t >= 0} be a centred homogeneous Gaussian field with almost surely continuous sample paths and correlation function r (s, t) = cov(X(s, t), X(0, 0)) such that r(s, t) = 1 - vertical bar s vertical bar(alpha 1) - vertical bar t vertical bar(alpha 2) + o(vertical bar s vertical bar(alpha 1) + vertical bar t vertical bar(alpha 2)), s,t -> 0, with alpha 1, alpha 2 is an element of(0,2], and r (s, t) < 1 for (s, t) not equal (0, 0). In this contribution we derive an asymptotic expansion (as u -> infinity) of P(sup((sn1(u),tn2(u))is an element of[0,x]x[0,y]) X(s,t)