Random Field Models in Earth Sciences

Name: Random Field Models in Earth Sciences
Brand: Dover Publications
Price: 45.69 EUR
Availability: OnlineOnly

George Christakos(Autor*in)

Dover Publications (Verlag)

1. Auflage

Erschienen am 9. August 2012

864 Seiten

E-Book

ePUB mit Adobe-DRM

Systemvoraussetzungen

978-0-486-16091-7 (ISBN)

45,69 €inkl. 7% MwSt.

Systemvoraussetzungen

für ePUB mit Adobe-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Person

Inhalt

Intro
Title Page
Copyright Page
Dedication
Table of Contents
Foreword
Preface
1 - Prolegomena
1. The Science of the Probable and the Random Field Model
2. The Physical Significance of the Random Field Model
3. The Mathematics of Random Fields
4. The Philosophical Theses of the Stochastic Research Program
5. The Practice of the Stochastic Research Program and the Spectrum of Its Applications
2 - The Spatial Random Field Model
1. Introduction
2. Basic Notions
3. Characterization of Spatial Random Fields by Means of Their Second-Order Statistical Moments-Correlation Theory
4. Certain Geometrical Properties of Spatial Random Fields
5. Spectral Characteristics of Spatial Random Fields
6. Auxiliary Hypotheses
7. Homogeneous Spatial Random Fields
8. Isotropic Spatial Random Fields
9. Scales of Spatial Correlation
10. Relationships between the Spatial and the Frequency Domains-The Uncertainty Principle
11. Spatial Random Fields with Homogeneous Increments
12. On the Ergodicity Hypotheses of Spatial Random Fields
13. Information and Entropy of Spatial Random Fields
3 - The Intrinsic Spatial Random Field Model
1. Introduction
2. Generalized Spatial Random Fields
3. Spatial Random Fields with Space Homogeneous Increments or Intrinsic Spatial Random Fields
4. Discrete Linear Representations of Spatial Random Fields
5. Stochastic Differential and Difference Equations
4 - The Factorable Random Field Model
1. Introduction
2. The Theory of Factorable Random Fields
3. Nonlinear Transformations of Factorable Random Fields
4. Construction of Factorable Random Fields
5. The Nonlinear State-Nonlinear Observation System
5 - The Spatiotemporal Random Field Model
1. Introduction
2. Spatiotemporal Natural Processes-A Review
3. Ordinary Spatiotemporal Random Fields
4. Generalized Spatiotemporal Random Fields
5. Spatiotemporal Random Fields of Order ?/µ, (Ordinary and Generalized)
6. Stochastic Partial Differential Equations
7. Discrete Linear Representations of Spatiotemporal Random Fields
6 - Space Transformations of Random Fields
1. Introduction
2. Space Transformations
3. Space Transformation Representations of Spatial Random Fields
4. Stochastic Differential Equation Models
5. Criteria of Permissibility
7 - Random Field Modeling of Natural Processes
1. Introduction
2. Descriptive Features of Natural Processes and the Basic Working Hypotheses
3. Duality Relations between the Natural Process and the Spatial Random Field Model-Examples from the Geosciences
4. Certain Practical Aspects of Spatial and Temporal Variability Characterization
5. Qualitative (Soft) Information
6. Some Final Comments about the Stochastic Research Program
8 - Simulation of Natural Processes
1. Introduction
2. The Physical Significance of Simulation
3. Simulation of Random Fields
4. Simulation of Spatial Random Field by Space Transformations-Examples
5. Techniques of One-Dimensional Simulation
6. Simulation of Integrated Natural Processes
7. Simulation of Dynamic Stochastic Systems
8. The Effect of Measurement Error
9. Simulation of Spatial Random Fields by Means of Frequency Domain Techniques
10. The Lower-Upper Triangular Matrix Technique
11. The Karhunen-Loeve Expansion Technique
12. Simulation of Vector Spatial Random Fields
13. Simulation of Non-Gaussian Spatial Random Fields
14. Simulation in Space-Time
9 - Estimation in Space and Time
1. Introduction
2. A Brief Review of Nonstochastic Estimators and the Emergence of Stochastic Estimation
3. Optimum Stochastic Spatial Estimation
4. Certain Classes of Linear Spatial Estimators
5. Properties and Physical Interpretations of Linear Spatial Estimators
6. Nonlinear Estimation
7. Optimal Estimation of Spatiotemporal Random Fields
8. A Bayesian/Maximum-Entropy View of the Estimation Problem
10 - Sampling Design
1. Introduction
2. About Sampling
3. Simple Global Approaches to Sampling Design
4. Optimal Linear Estimation Approaches to Global Sampling Design
5. Local Sampling Design Approaches
6. Statistical Inference Problems in Sampling Design
7. The Design of Spatiotemporal Sampling Networks
8. A Taxonomy of Site Exploration Tasks
9. Terminal Decision Analysis and Sampling Design
References
Index
A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS

Systemvoraussetzungen

Als PDF speichern Als Link merken