Ubiquity of, and geostatistics for, nonstationary increment random fields

Nonstationary random fields such as fractional Brownian motion and fractional Levy motion have been studied extensively in the hydrology literature. On the other hand, random fields that have nonstationary increments have seen little study. A mathematical argument is presented that demonstrates processes with stationary increments are the exception and processes with nonstationary increments are far more abundant. The abundance of nonstationary increment processes has important implications, e.g., in kriging where a translation-invariant variogram implicitly assumes stationarity of the increments. An approach to kriging for processes with nonstationary increments is presented and accompanied by some numerical results.