Spatiotemporal Random Fields, Second Edition: Theory and Applications

✍ Scribed by George Christakos

• Publisher: Elsevier Science
• Year: 2017
• Tongue: English
• Leaves: 698
• Edition: 2nd ed
• Category: Library

✦ Synopsis

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.

• Contains applications in the form of examples and case studies, providing readers with first-hand experiences
• Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas
• Includes significant updates from the previous edition, including a focus on new theoretical and applied results

✦ Table of Contents

Content: Front Cover
Spatiotemporal Random Fields
Spatiotemporal Random FieldsTheory and Applications
Copyright
Dedication
Contents
Preface
I --
SPACE, TIME, SPACE-TIME, RANDOMNESS, AND PROBABILITY
1. INTRODUCTION
2. SPACE-TIME CONTINUUM AND KOLMOGOROV PROBABILITY SPACE
2.1 SPACE-TIME ARGUMENTS: POINTS, LAGS, SEPARATIONS, AND METRICS
2.2 TRANSFORMATIONS AND INVARIANCE IN SPACE-TIME
2.3 SPACE-TIME INTERPRETATIONS
2.4 FUNCTIONS OF SPACE-TIME ARGUMENTS
3. RANDOM VARIABLES IN SPACE-TIME
3.1 KOLMOGOROV'S PROBABILITY THEORY
3.2 USEFUL INEQUALITIES
3.3 CONVERGENCE OF RANDOM VARIABLE SEQUENCES. II --
SPATIOTEMPORAL RANDOM FIELDS1. INTRODUCTION
1.1 THE SPACE-TIME COMPONENT
1.2 THE RANDOMNESS COMPONENT
2. CHARACTERIZATION OF SCALAR SPATIOTEMPORAL RANDOM FIELDS
2.1 PROBABILISTIC STRUCTURE
2.2 THE CHARACTERISTIC FUNCTION
2.3 SPATIOTEMPORAL VARIABILITY FUNCTIONS: COMPLETE (OR FULL) AND PARTIAL
2.4 ANALYSIS IN THE SPECTRAL DOMAIN
2.5 DATA-INDEPENDENT SPATIOTEMPORAL VARIABILITY FUNCTION
2.6 SOME NOTICEABLE SPECIAL CASES OF THE SPATIOTEMPORAL RANDOM FIELD THEORY
2.7 SPACE-TIME SEPARABILITY
3. PHYSICAL INSIGHT BEHIND THE RANDOM FIELD CONCEPT
3.1 RANDOM FIELD REALIZATIONS. 3.2 PROBABLE VERSUS ACTUAL3.3 PROBABILITY AND THE OBSERVATION EFFECT
3.4 SELF-CONSISTENCY AND PHYSICAL FIDELITY
4. GEOMETRY OF SPATIOTEMPORAL RANDOM FIELDS
5. VECTOR SPATIOTEMPORAL RANDOM FIELDS
6. COMPLEX SPATIOTEMPORAL RANDOM FIELDS
7. CLASSIFICATIONS OF THE SPATIOTEMPORAL RANDOM FIELD MODEL
7.1 FIRST CLASSIFICATION: DISCRETE VERSUS CONTINUOUS ARGUMENTS
7.2 SECOND CLASSIFICATION: SCALAR VERSUS VECTOR RANDOM FIELDS AND ARGUMENTS
7.3 THIRD CLASSIFICATION: PROBABILITY LAW SHAPES
7.4 FOURTH CLASSIFICATION: SPACE-TIME VARIABILITY. 7.5 FIFTH CLASSIFICATION: SPATIOTEMPORAL RANDOM FIELD MEMORY VERSUS INDEPENDENCE8. CLOSING COMMENTS
8.1 THE METHODOLOGICAL IMPORTANCE OF SPACE-TIME
8.2 A CONCEPTUAL MEETING POINT FOR MODELERS AND EXPERIMENTALISTS
8.3 THERE IS NO ASSUMPTIONLESS MODELING
III --
SPACE-TIME METRICS
1. BASIC NOTIONS
1.1 FORMAL AND PHYSICAL ASPECTS OF SPACE-TIME METRIC DETERMINATION
1.2 SPACE-TIME METRIC FORMS
1.3 DERIVED SPACE-TIME METRICS
1.4 SPACE-TIME METRIC DIFFERENTIALS
1.5 SPECIFYING SPACE-TIME RELATIONSHIPS IN THE COVARIANCE FUNCTION
2. COVARIANCE DIFFERENTIAL FORMULAS. 3. SPACE-TIME METRIC DETERMINATION FROM PHYSICAL CONSIDERATIONS4. EXAMPLES
5. CONCERNING THE ZETA COEFFICIENTS
6. CLOSING COMMENTS
IV --
SPACE-TIME CORRELATION THEORY
1. FOCUSING ON SPACE-TIME VARIABILITY FUNCTIONS
1.1 BASICS OF SPACE-TIME CORRELATION THEORY
1.2 PHYSICAL INVESTIGATIONS BASED ON SPACE-TIME CORRELATION THEORY
2. SPACE-TIME VARIABILITY FUNCTIONS IN TERMS OF SCALAR SPACE-TIME STATISTICS
2.1 LOCALITY: ONE-POINT SPACE-TIME VARIABILITY FUNCTIONS
2.2 NONLOCALITY: OMNIDIRECTIONAL TWO-POINT SPACE-TIME VARIABILITY FUNCTIONS.