Spatiotemporal Random Fields: Theory and Applications

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others.

The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty.

1. Space, Time, Spacetime, Randomness, and Probability 2. Spatiotemporal Random Fields - S/TRFs 3. Space-Time Metrics 4. Space-Time Correlation Theory 5. Transformations of Spatiotemporal Random Fields 6. Geometrical Properties of Spatiotemporal Random Fields 7. Auxiliary Hypotheses of Spatiotemporal Variation 8. Isostationary Scalar Spatiotemporal Random Fields 9. Vector and Multivariate Random Fields 10. Special Classes of Spatiotemporal Random Fields 11. Construction of Spatiotemporal Probability Laws 12. Spatiotemporal Random Functionals 13. Generalized Spatiotemporal Random Fields 14. Physical Considerations 15. Permissibility in Space-Time 16. Construction of Spatiotemporal Covariance Models