# Parametric stationary covariance models¶

*multivariate Exponential model*as one of the possible parametric models for the covariance function .

**The multivariate exponential model**

This model defines the covariance function by:

(1)¶

where is a correlation matrix, is defined by:

(2)¶

and is defined by:

(3)¶

with and for any .

We call the amplitude vector and the scale vector. The expression of is the combination of:

the matrix that models the spatial correlation between the components of the process at any vertex (since the process is stationary):

(4)¶

the matrix that models the correlation between the marginal random variables and :

the matrix that models the variance of each marginal random variable:

This model is such that:

(5)¶

It is possible to define the exponential model from the spatial covariance matrix rather than the correlation matrix :

(6)¶

API:

See

`ExponentialModel`

See

`MaternModel`