  Cokriging is the common method of spatial interpolation (best linear unbiased
prediction) in multivariate geostatistics. While best linear prediction has
been well understood in univariate spatial statistics, the literature for the
multivariate case has been elusive so far. The new challenges provided by
modern spatial datasets, being typically multivariate, call for a deeper study
of cokriging. In particular, we deal with the problem of misspecified cokriging
prediction within the framework of fixed domain asymptotics. Specifically, we
provide conditions for equivalence of measures associated with multivariate
Gaussian random fields, with index set in a compact set of a d-dimensional
Euclidean space. Such conditions have been elusive for over about 50 years of
spatial statistics.
  We then focus on the multivariate Mat\'ern and Generalized Wendland classes
of matrix valued covariance functions, that have been very popular for having
parameters that are crucial to spatial interpolation, and that control the mean
square differentiability of the associated Gaussian process. We provide
sufficient conditions, for equivalence of Gaussian measures, relying on the
covariance parameters of these two classes. This enables to identify the
parameters that are crucial to asymptotically equivalent interpolation in
multivariate geostatistics. Our findings are then illustrated through
simulation studies.
