# zbMATH — the first resource for mathematics

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
##### Keywords:
maximum; Fernique’s condition; sample continuity
Full Text: