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On the equivalence of Gaussian processes with factorable covariance functions

Let {Xt}teT be a Gaussian process on a probability space (Q, Y, 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 {Xt}teT is a Gaussian process is equivalent to a probability measure P.