On certain classes of spatiotemporal random fields with applications to space-time data processing

A theory of spatiotemporal random fields is developed as an extension of the Ito-Gel'fand theory of random distributions. Notable characteristics of the most important classes of spatiotemporal fields are examined. The theory is used to describe the correlation structure of generally space nonhomogeneous/time nonstationary processes and to derive optimal estimators for data dispersed simultaneously in space and time. A variety of applications of subtemporal data processing are reviewed. The outcomes of this processing may be not an end in themselves. In several situations they will be the valuable inputs to decision-making processes, risk evaluation methods, control and investment policies, etc