Strict Stationarity

A random function is said to be stationary, in the strict sense, if its spatial law is invariant under translation. More precisely, the two $k$-component vectorial random variables $/{Z({/boma x}_{1}), Z({/boma x}_{2}), /ldots, Z({/boma x}_{k})/}$ and $/{Z({/boma x}_{1}+{/boma h}),Z({/boma x}_{2}+{/boma h}), /ldots, Z({/boma x}_{k}+{/boma h})/}$ are identical in law (have the same $k$-variable distribution law) whatever the translation vector ${/boma h}$.

However, in linear geostatistics, as we are only interested in the previously defined two first-order moments, it will be enough to assume first that these moments exist, and then to limit the stationarity assumptions to them.