Covariance Function - Simplifications With Stationarity

Simplifications With Stationarity

In case of a weakly stationary random field, where

for any lag h, the covariance function can be represented by a one-parameter function

which is called a covariogram and also a covariance function. Implicitly the C(x_i, x_j) can be computed from C_s(h) by:

The positive definiteness of this single-argument version of the covariance function can be checked by Bochner's theorem.