# Estimation of a non stationary cov. modelΒΆ

Let be a multivariate normal process of dimension where . is supposed to be a second order process and we note its covariance function. We denote the vertices of the common mesh and the associated values of the field . We suppose that we have fields. We recall that the covariance function writes:

(1)ΒΆ

where the mean function is defined by:

(2)ΒΆ

First, we estimate the covariance function on the vertices of the mesh . At each vertex , we use the empirical mean estimator applied to the fields to estimate:

at the vertex :

(3)ΒΆ

at the vertices :

(4)ΒΆ

Then, we build a covariance function defined on which is a piecewise constant function defined on by:

where is such that is the vertex of the nearest to and the nearest to .