Spatiotemporal random fields: theory and applications

"Features detailed information on spatiotemporal random field theory; including ordinary and generalized models and techniques in the physical and the spectral domains ... Second Edition, provides readers with new and updated content 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 heterogeneous. 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"--Back cover.

Space, time, space -- time, randomness, and probability -- Spatiotemporal random fields -- Space-time metrics -- Space-time correlation theory -- Transformations of spatiotemporal random fields -- Geometrical properties of spatiotemporal random fields -- Auxiliary hypotheses of spatiotemporal variation -- Isostationary scalar spatiotemporal random fields -- Vector and multivariate random fields -- Special classes of spatiotemporal random fields -- Construction of spatiotemporal probability laws -- Spatiotemporal random functionals -- Generalized spatiotemporal random fields -- Physical considerations -- Permissibility in space-time -- Construction of spatiotemporal covariance models.