Spatiotemporal random fields: theory and applications

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.