On the equivalence of Gaussian processes with factorable covariance functions

Abstract:

Let ${\{ {X_t}\} _{t \in T}}$ be a Gaussian process on a probability space $(\Omega ,\mathcal {F},P)$ with a factorable covariance function. We assume here that T is a p-dimensional Euclidean space. The purpose of this paper is to give necessary and sufficient conditions that a probability measure Q with respect to which ${\{ {X_t}\} _{t \in T}}$ is a Gaussian process is equivalent to a probability measure P.