ABSTRACT
The term stochastic typically refers to processes that are distributed in time (e.g., financial option prices), space (e.g., mineral concentrations), or both (e.g., groundwater pollutant concentrations). For spatially distributed variables the term spatial random fields is used, while for time evolution the term stochastic process is preferred. For space-time dependence the term space-time random fields is common. Correlations are important for many engineering applications, because they allow statistical prediction at points where measurements are not available, giving engineers the ability to design optimal exploitation strategies for mines and to estimate the environmental risk from the dispersion of toxic pollutants in the groundwater. Hence, randomness does not exclude predictability but implies a statistical distribution of the predictions, which must be accompanied by a measure of the associated uncertainty.
