Equivalence of Gaussian measures of multivariate random fields

Problems related to weather forecast, forest attributes estimation and prediction, disease propagation, among others, are commonly approximated in the framework of multivariate Gaussian random field modeling. This paper deals with the equivalence condition of two zero-mean Gaussian infinite-dimensional vector measures defined on the finite product of separable Hilbert spaces. In particular, sufficient conditions are provided. The results derived are applied to obtain the equivalence of Gaussian measures associated with two stationary zero-mean Gaussian vector random fields. Classical problems related to, for example, asymptotic properties of maximum likelihood vector Gaussian random field parameter estimators from tapered multivariate covariance functions, often arising in Multivariate Geostatistics, can be solved as direct application of the results derived.