Abstract

Positive definite kernels are fundamental in environmental statistics. Usually they are constructed over the Euclidean space, but in a more general context, they should be constructed over Riemannian manifolds. Theory concerning this case is dispersed. Therefore, the outline of this work is to provide a background on fundamental definitions and theorems related to the construction of positive definite kernels from the Riemannian geometry perspective, putting special emphasis on the Riemannian manifold that arises from the product of the n-dimensional sphere with the real line or a closed interval, in order to study space-time random processes on the sphere.