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The maximum of a Gaussian process with nonconstant variance. (English) Zbl 0577.60036
The author considers a mean zero Gaussian field over \([0,1]^ n\) whose variance has a unique maximum at some point \(\tau\). Under weak conditions related to Fernique’s condition for sample continuity, it is shown that for \(u\to \infty\) \[ P(\max_{t\in [0,1]^ n}X(t)>u)\sim P(X(\tau)>u). \]
Reviewer: J.Cuzick

MSC:
60G17 Sample path properties
60G15 Gaussian processes
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