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E-raamat: Spatiotemporal Random Fields: Theory and Applications

(Professor, San Diego State University, USA and Zhejiang University, China)
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  • Ilmumisaeg: 26-Jul-2017
  • Kirjastus: Elsevier Science Publishing Co Inc
  • Keel: eng
  • ISBN-13: 9780128030325
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Spatiotemporal Random Fields: Theory and ApplicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 26-Jul-2017
  • Kirjastus: Elsevier Science Publishing Co Inc
  • Keel: eng
  • ISBN-13: 9780128030325
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Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of random field models and stochastic data processing to problems in hydrogeology, geostatistics, climate modeling, and oil reservoir engineering, among others. The new edition features considerable detail of random field theory, including ordinary and generalized, as well as spatial and spatiotemporal approaches. Presenting new theoretical and applied results, with particular emphasis on integrated spatiotemporal analysis, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time dependence 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.Authored by an internationally renowned scientist and a leader in the field of spatial statisticsContains a considerable amount of applications in the form of examples and case studies, providing readers with first-hand experiencesPresents an easy to follow narrative which progresses from simple concepts to more challenging onesIncludes significant updates since the previous edition including a focus on new theoretical and applied results

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Features detailed information on spatiotemporal random field theory, including ordinary and generalized models and techniques in the physical and the spectral domains
Preface xv
Chapter I Space, Time, Space-Time, Randomness, and Probability
1(38)
1 Introduction
1(3)
2 Space---Time Continuum and Kolmogorov Probability Space
4(27)
2.1 Space---Time Arguments: Points, Lags, Separations, and Metrics
4(13)
2.2 Transformations and Invariance in Space---Time
17(6)
2.3 Space---Time Interpretations
23(3)
2.4 Functions of Space---Time Arguments
26(5)
3 Random Variables in Space---Time
31(8)
3.1 Kolmogorov's Probability Theory
31(4)
3.2 Useful Inequalities
35(2)
3.3 Convergence of Random Variable Sequences
37(2)
Chapter II Spatiotemporal Random Fields
39(44)
1 Introduction
40(2)
1.1 The Space---Time Component
41(1)
1.2 The Randomness Component
42(1)
2 Characterization of Scalar Spatiotemporal Random Fields
42(19)
2.1 Probabilistic Structure
43(7)
2.2 The Characteristic Function
50(1)
2.3 Spatiotemporal Variability Functions: Complete (or Full) and Partial
51(5)
2.4 Analysis in the Spectral Domain
56(1)
2.5 Data-Independent Spatiotemporal Variability Function
57(2)
2.6 Some Noticeable Special Cases of the Spatiotemporal Random Field Theory
59(1)
2.7 Space---Time Separability
60(1)
3 Physical Insight Behind the Random Field Concept
61(8)
3.1 Random Field Realizations
61(2)
3.2 Probable Versus Actual
63(1)
3.3 Probability and the Observation Effect
64(1)
3.4 Self-consistency and Physical Fidelity
65(4)
4 Geometry of Spatiotemporal Random Fields
69(1)
5 Vector Spatiotemporal Random Fields
70(3)
6 Complex Spatiotemporal Random Fields
73(1)
7 Classifications of the Spatiotemporal Random Field Model
73(5)
7.1 First Classification: Discrete Versus Continuous Arguments
74(1)
7.2 Second Classification: Scalar Versus Vector Random Fields and Arguments...
74(1)
7.3 Third Classification: Probability Law Shapes
74(1)
7.4 Fourth Classification: Space---Time Variability
75(2)
7.5 Fifth Classification: Spatiotemporal Random Field Memory Versus Independence
77(1)
8 Closing Comments
78(5)
8.1 The Methodological Importance of Space---Time
78(2)
8.2 A Conceptual Meeting Point for Modelers and Experimentalists
80(1)
8.3 There Is No Assumptionless Modeling
81(2)
Chapter III Space-Time Metrics
83(38)
1 Basic Notions
83(17)
1.1 Formal and Physical Aspects of Space---Time Metric Determination
84(3)
1.2 Space---Time Metric Forms
87(5)
1.3 Derived Space---Time Metrics
92(1)
1.4 Space---Time Metric Differentials
93(2)
1.5 Specifying Space---Time Relationships in the Covariance Function
95(5)
2 Covariance Differential Formulas
100(6)
3 Space---Time Metric Determination From Physical Considerations
106(2)
4 Examples
108(9)
5 Concerning the Zeta Coefficients
117(1)
6 Closing Comments
118(3)
Chapter IV Space-Time Correlation Theory
121(34)
1 Focusing on Space---Time Variability Functions
121(3)
1.1 Basics of Space---Time Correlation Theory
122(1)
1.2 Physical Investigations Based on Space---Time Correlation Theory
123(1)
2 Space---Time Variability Functions in Terms of Scalar Space---Time Statistics
124(15)
2.1 Locality: One-Point Space---Time Variability Functions
125(2)
2.2 Nonlocality: Omnidirectional Two-Point Space---Time Variability Functions
127(6)
2.3 Nonlocality: Direction-Specific Space---Time Variability Functions
133(1)
2.4 Physical Considerations and Assumptions of Space---Time Variability Functions
133(4)
2.5 Formal and Physical Covariance Permissibility
137(2)
3 Basic Properties of Covariance Functions
139(2)
4 Cross---Space---Time Variability Functions
141(3)
5 Correlation of Gaussian and Related Spatiotemporal Random Fields
144(2)
5.1 General Considerations
144(1)
5.2 Gaussian Properties
144(2)
6 Correlation Theory of Complex Spatiotemporal Random Fields
146(9)
6.1 Basic Notions
146(2)
6.2 Other Types of Complex Covariance Functions
148(3)
6.3 Gaussian Complex Spatiotemporal Random Fields
151(1)
6.4 Complex-Valued Versus Real-Valued Covariance Functions of Space---Time Homostationary Random Fields
152(1)
6.5 Some Methodological Considerations
153(2)
Chapter V Transformations of Spatiotemporal Random Fields
155(48)
1 Introduction
155(2)
2 Fourier Transformation
157(11)
2.1 Characteristic Functions
157(1)
2.2 Harmonizable Random Fields and Covariance Functions
158(7)
2.3 Transfer Function and Evolutionary Mean Power
165(2)
2.4 Fourier Transform of Vector Spatiotemporal Random Fields
167(1)
3 Space Transformation
168(12)
3.1 Basic Notions
168(5)
3.2 Space Transformation of Spatiotemporal Random Fields
173(2)
3.3 Space Transformation for Spatiotemporal Variability Functions
175(2)
3.4 Space Transformation in the Simulation of Spatiotemporal Random Fields
177(3)
3.5 Space Transformation in the Solution of Stochastic Partial Differential Equation
180(1)
4 The Traveling Transformation
180(21)
4.1 Basic Notions
181(5)
4.2 Determination of the Traveling Vector
186(9)
4.3 Traveling Transformation in Spatiotemporal Random Field Estimation: The Space---Time Projection Technique
195(6)
5 Closing Comments
201(2)
Chapter VI Geometrical Properties of Spatiotemporal Random Fields
203(36)
1 Introduction
203(1)
2 Stochastic Convergence
204(4)
3 Stochastic Continuity
208(8)
3.1 Basic Types of Stochastic Continuity
209(3)
3.2 Equivalence, Modification, and Separability
212(4)
4 Stochastic Differentiation
216(17)
4.1 Basic Notation and Definitions
217(6)
4.2 Covariances of Random Field Derivatives
223(4)
4.3 Mean Squarely Differentiability Conditions
227(4)
4.4 Almost Surely Differentiability Conditions
231(2)
5 The Central Limit Theorem
233(1)
6 Stochastic Integration
234(5)
Chapter VII Auxiliary Hypotheses of Spatiotemporal Variation
239(64)
1 Introduction
239(11)
1.1 Hypothesis 1: Homostationarity
241(2)
1.2 Hypothesis 2: Isostationarity
243(2)
1.3 Hypothesis 3: Heterogeneity
245(1)
1.4 Hypothesis 4: Ergodicity
246(2)
1.5 Hypothesis 5: Separability
248(1)
1.6 Hypothesis 6: Symmetry
249(1)
1.7 Hypothesis 7: Locational Divergence
249(1)
2 Space---Time Homostationarity
250(10)
2.1 Omnidirectional Spatiotemporal Variability Functions
251(4)
2.2 Direction-Specific Spatiotemporal Covariance Function
255(1)
2.3 Anisotropic Features
255(2)
2.4 Spatiotemporal Variogram and Structure Functions: Omnidirectional and Direction Specific
257(3)
3 Spectral Representations of Space---Time Homostationarity
260(16)
3.1 Spectral Functions of Space---Time Homostationary Random Fields
261(5)
3.2 Properties of the Spectral Density Function
266(2)
3.3 Partial Spectral Representations
268(4)
3.4 More on Dispersion Relations
272(1)
3.5 Separability Aspects
273(3)
4 The Geometry of Space---Time Homostationarity
276(21)
4.1 Differentiation Formulas: Physical and Spectral Domains
276(9)
4.2 Stochastic Continuity and Differentiability
285(11)
4.3 Spatiotemporal Random Field Integrability
296(1)
5 Spectral Moments and Linear Random Field Transformations
297(6)
Chapter VIII Isostationary Scalar Spatiotemporal Random Fields
303(44)
1 Introduction
303(11)
1.1 Basic Considerations
303(6)
1.2 Power-Law Correlations
309(4)
1.3 Physical Considerations of Variogram Functions
313(1)
2 Relationships Between Covariance Derivatives and Space---Time Isostationarity
314(5)
3 Higher-Order Spatiotemporal Variogram and Structure Functions
319(1)
4 Separable Classes of Space---Time Isostationary Covariance Models
320(4)
5 A Survey of Space---Time Covariance Models
324(5)
6 Scales of Spatiotemporal Dependence and the Uncertainty Principle
329(7)
6.1 Scales for Spatiotemporal Random Fields With Restricted Space---Time Variability
330(4)
6.2 Relationships Between Physical and Spectral Domains: The Uncertainty Principle
334(2)
7 On the Ergodicity Hypotheses of Spatiotemporal Random Fields
336(11)
Chapter IX Vector and Multivariate Random Fields
347(36)
1 Introduction
347(2)
2 Homostationary and Homostationarily Connected Cross---Spatiotemporal Variability Functions and Cross---Spectral Density Functions
349(7)
2.1 Basic Notions and Interpretations
350(5)
2.2 Geometry of Vector Spatiotemporal Random Fields
355(1)
3 Some Special Cases of Covariance Functions
356(6)
4 Solenoidal and Potential Vector Spatiotemporal Random Fields
362(3)
5 Partial Cross-Covariance and Cross-Spectral Functions
365(1)
6 Higher-Order Cross---Spatiotemporal Variability Functions
366(3)
7 Isostationary Vector Spatiotemporal Random Fields
369(12)
7.1 Direct (Lag-Based) Space---Time Isostationarity
369(3)
7.2 Composite Lag-Field---Based Space---Time Isostationarity
372(6)
7.3 Links With Solenoidal and Potential Spatiotemporal Random Fields
378(3)
8 Effective Distances and Periods
381(2)
Chapter X Special Classes of Spatiotemporal Random Fields
383(26)
1 Introduction
383(1)
2 Frozen Spatiotemporal Random Fields and Taylor's Hypothesis
384(16)
2.1 Basic Notions
385(4)
2.2 Spectral Domain Analysis
389(2)
2.3 Differential Equation Representations
391(4)
2.4 Extensions of the Frozen Random Field Model
395(4)
2.5 Integrals of Frozen Spatiotemporal Random Fields
399(1)
2.6 Vector Frozen Spatiotemporal Random Fields
399(1)
3 Plane-Wave Spatiotemporal Random Fields
400(2)
4 Lognormal Spatiotemporal Random Fields
402(1)
5 Spherical Spatiotemporal Random Fields
402(5)
6 Lagrangian Spatiotemporal Random Fields
407(2)
Chapter XI Construction of Spatiotemporal Probability Laws
409(24)
1 Introduction
409(2)
2 Direct Probability Density Model Construction Techniques
411(3)
2.1 The Independency Techniques
412(1)
2.2 The Spherical Symmetry Technique
412(1)
2.3 The Transformation Technique
413(1)
3 Factora-Based Probability Density Model Construction Techniques
414(4)
4 Copula-Based Probability Density Model Construction Techniques
418(3)
5 Stochastic Differential Equation---Based Probability Density Model Construction Techniques
421(7)
5.1 The Transformation of Variables Approach
422(3)
5.2 The Characteristic Function Approach
425(1)
5.3 The Functional Approach
426(2)
6 Bayesian Maximum Entropy---Based Multivariate Probability Density Model Construction Techniques
428(3)
7 Methodological and Technical Comments
431(2)
Chapter XII Spatiotemporal Random Functionals
433(22)
1 Continuous Linear Random Functionals in the Space---Time Domain
433(14)
1.1 Basic Notions
433(3)
1.2 Generalized Fourier Transform
436(3)
1.3 Space---Time Characteristic Functionals
439(2)
1.4 Functional Derivatives
441(6)
2 Gaussian Functionals
447(8)
Chapter XIII Generalized Spatiotemporal Random Fields
455(46)
1 Basic Notions
455(13)
1.1 The Notion of Generalized Spatiotemporal Random Field
456(5)
1.2 Generalized Spatiotemporal Random Field Properties and Physical Significance
461(3)
1.3 Homostationary Generalized Spatiotemporal Random Fields
464(4)
2 Spatiotemporal Random Fields of Orders v/μ
468(9)
2.1 Departure From Space---Time Homostationarity
468(2)
2.2 Space-Time Detrending
470(4)
2.3 Ordinary Spatiotemporal Random Field-v/μ Representations of the Generalized Spatiotemporal Random Field-v/μ
474(1)
2.4 Determination of the Operator Qv/μ and Its Physical Significance
475(2)
3 The Correlation Structure of Spatiotemporal Random Field-v/μ
477(13)
3.1 Space-Time Functional Statistics
477(2)
3.2 Generalized Spatiotemporal Covariance Functions
479(2)
3.3 Generalized Spectral Representations and Permissibility of Generalized Covariances
481(3)
3.4 Generalized Covariance Function Models
484(6)
4 Discrete Linear Representations of Spatiotemporal Random Fields
490(11)
4.1 Space---Time Random Increments
490(5)
4.2 Space---Time Variogram Analysis
495(6)
Chapter XIV Physical Considerations
501(20)
1 Spatiotemporal Variation and Laws of Change
501(3)
2 Empirical Algebraic Equations
504(2)
3 Physical Differential Equations
506(6)
4 Links Between Stochastic Partial Differential Equation and Generalized Random Fields
512(6)
4.1 Links in Terms of the Random Functional
513(2)
4.2 Links in Terms of the Detrending Operator
515(3)
5 Physical Constraints in the Form of Integral Relationships, Domain Restrictions, and Dispersion Equations
518(3)
Chapter XV Permissibility in Space-Time
521(22)
1 Concerning Permissibility
521(1)
2 Bochnerian Analysis
522(6)
2.1 Main Results
523(2)
2.2 Limitations of Bochnerian Analysis
525(3)
3 Metric Dependence
528(1)
4 Formal and Physical Permissibility Conditions for Covariance Functions
529(11)
4.1 Permissibility Conditions for Space---Time Homostationary Covariance Functions
530(2)
4.2 Permissibility Conditions for Space---Time Isostationary Covariance Functions
532(3)
4.3 Permissibility Conditions for Generalized Spatiotemporal Covariance Functions
535(2)
4.4 Permissibility Conditions for Spatiotemporal Covariance Matrices
537(3)
5 More Consequences of Permissibility
540(3)
Chapter XVI Construction of Spatiotemporal Covariance Models
543(54)
1 Introduction
543(2)
2 Probability Density Function---Based and Related Techniques
545(7)
2.1 Linking Directly Covariance Models and Probability Density Functions
545(3)
2.2 Using Polynomial-Exponential Functions
548(2)
2.3 Using Spectral Functions
550(2)
3 Delta and Related Techniques
552(5)
3.1 Basic Decomposition
552(2)
3.2 Normalized Angular Spectrum Decomposition
554(1)
3.3 Normalized Frequency Spectrum (or Coherency Function) Decomposition
555(2)
4 Space Transformation Technique
557(3)
5 Physical Equation Techniques
560(12)
5.1 Covariance Construction From Stochastic Partial Differential Equation Representations
560(10)
5.2 Covariance Construction From Algebraic Empirical Relationships
570(2)
6 Closed-Form Techniques
572(8)
7 Integral Representation Techniques
580(2)
8 Space---Time Separation Techniques
582(4)
9 Dynamic Formation Technique
586(1)
10 Entropic Technique
587(1)
11 Attribute and Argument Transformation Techniques
588(2)
11.1 Attribute Transformation
588(1)
11.2 Argument Transformation
589(1)
12 Cross-Covariance Model Construction Techniques
590(3)
13 Revisiting the Role of Physical Constraints
593(1)
14 Closing Comments
594(3)
Exercises 597(46)
References 643(10)
Appendix 653(12)
Index 665
George Christakos is a Professor in the Department of Geography at San Diego State University (USA) and in the Institute of Island & Coastal Ecosystems, Ocean College at Zhejiang University (China). He is an expert in spatiotemporal random field modeling of natural systems, and his teaching and research focus on the integrative analysis of natural phenomena; spatiotemporal random field theory; uncertainty assessment; pollution monitoring and control; human exposure risk and environmental health; space-time statistics and geostatistics.
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