Berman, Simeon M. The maximum of a Gaussian process with nonconstant variance. (English) Zbl 0577.60036 Ann. Inst. Henri Poincaré, Probab. Stat. 21, 383-391 (1985). 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 Cited in 8 Documents MSC: 60G17 Sample path properties 60G15 Gaussian processes Keywords:maximum; Fernique’s condition; sample continuity PDFBibTeX XMLCite \textit{S. M. Berman}, Ann. Inst. Henri Poincaré, Probab. Stat. 21, 383--391 (1985; Zbl 0577.60036) Full Text: Numdam EuDML