The maximum of a Gaussian process with nonconstant variance (Q1065456)
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scientific article; zbMATH DE number 3923775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The maximum of a Gaussian process with nonconstant variance |
scientific article; zbMATH DE number 3923775 |
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The maximum of a Gaussian process with nonconstant variance (English)
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1985
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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 \(u\to \infty\) \[ P(\max_{t\in [0,1]^ n}X(t)>u)\sim P(X(\tau)>u). \]
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maximum
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Fernique's condition
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sample continuity
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