Intrinsic Hypothesis

A random function $Z({/boma x})$ is said to be intrinsic if:

(i)

the mathematical expectation exists and does not depend on the support point $/boma{x}$,

(ii)

for all vectors ${/boma h}$ the increment [ $Z({/boma x}+{/boma h})-Z({/boma x})$] has a finite variance which does not depend on ${/boma x}$,

Thus, second-order stationarity implies the intrinsic hypothesis, but the converse is not true: the intrinsic hypothesis can also be seen as the limitation of the second-order stationarity to the increments of the random function $Z({/boma x})$.

In practice, the structural function, covariance or variogram, is only used for limited distances $/vert{/boma h}/vert / < b$. The limit $b$ represents, for example, the diameter of the neighborhood of estimation (i.e., the zone which contains the information to be used). In such a case we speak of quasi-stationarity.