  We consider maximum likelihood estimation with data from a bivariate Gaussian
process with a separable exponential covariance model under fixed domain
asymptotic. We first characterize the equivalence of Gaussian measures under
this model. Then consistency and asymptotic distribution for the microergodic
parameters are established. A simulation study is presented in order to compare
the finite sample behavior of the maximum likelihood estimator with the given
asymptotic distribution.
