On the distribution of the maximum of a Gaussian field with d parameters
On the distribution of the maximum of a Gaussian field with d parameters
Let I be a compact d-dimensional manifold, let X:I→ℛ be a Gaussian process with regular paths and let FI(u), u∈ℛ, be the probability distribution function of sup t∈IX(t). We prove that under certain regularity and nondegeneracy conditions, FI is a C1-function and satisfies a certain implicit equation that permits to …