Double extremum probability for Gaussian stationary process (Q1851508)
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scientific article; zbMATH DE number 1851286
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Double extremum probability for Gaussian stationary process |
scientific article; zbMATH DE number 1851286 |
Statements
Double extremum probability for Gaussian stationary process (English)
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8 January 2003
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Let \(X(t)\) be the stationary Gaussian process with zero average which is determined on the whole direct line. Let \([T_1,T_2]\) and \([T_3,T_4]\) be nonintersecting segments on the direct line such that \(0<T_1<T_2<T_3<T_4\). The author presents an exact asymptotic behavior of the probability \(\mathbf P(\max_{t\in[T_1,T_2]} X(t)>u\), \(\max_{t\in[T_3,T_4]} X(t)>u)\) as \(u\to\infty\).
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0.8500124216079712
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0.829988956451416
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