Summary: On the Distribution of the Maximum of a Gaussian
Field with d Parameters
November 10, 2003
AMS subject classification: 60G15, 60G70.
Short Title: Distribution of the Maximum.
Key words and phrases: Gaussian fields, Rice Formula, Regularity of the Distri-
bution of the Maximum.
Let I be a compact d-dimensional manifold, X : I R a Gaussian
process with regular paths and FI(u) , u R the probability distribution
function of suptI X(t).
We prove that under certain regularity and non-degeneracy conditions, FI
is a C1-function and FI is absolutely continuous, and that FI FI satisfy
certain implicit equations that permit to give bounds for their values and to
compute their asymptotic behaviour as u +. This is a partial extension