Author(s): A.M. Yaglom
Publisher: Springer
Year: 1987
Title page
Preface
Introduction
CHAPTER 1 Basic Properties of Stationary Random Functions
1. Definition of a Random Function
2. Moments of a Random Function. Correlation Theory
3. Stationarity
4. Properties of Correlation Functions. Derivative and Integral of a Random Process
5. Complex Random Functions. Spaces of Random Variables
CHAPTER 2 Examples of Stationary Random Functions. Spectral Representations
6. Examples of Stationary Random Sequences
7. Examples of Stationary Random Processes
8. Spectral Representation of Stationary Random Processes
9. Spectral Representation of the Correlation Function
10. Examples of Correlation Functions of Stationary Processes
11. Linear Transformations of Stationary Random Processes
12. Examples of Linear Transformations of Stationary Processes
13. Spectral Representation of Stationary Sequences and Their Correlation Functions
14. Discrete Samples of Random Processes and Discrete Linear Transformations
15. Examples of Discrete Linear Transformations and Correlation Functions of Stationary Sequences
CHAPTER 3 Determination of the Statistical Characteristics of a Stationary Random Function from Experimental Data
16. Determination of the Mean Value of a Stationary Function X(t)
17. Determination of the Mean Square and Correlation Function of X(t)
18. Statistical Spectral Analysis. Determination of the Spectral Density Function
19. Some Practical Aspects and Additional Methods of Statistical Spectral Analysis. Detennination of the Spectral Distribution Function
CHAPTER 4 Some Generalizations of the Concepts of a Stationary Random Function and of a Spectral Representation
20. Multidimensional Stationary Random Functions
21. Homogeneous Random Fields
21.1 One-Dimensional and Multidimensional Homogeneous Random Fields
21.2 Statisticallnference for Homogeneous Fields
22. Isotropie Random Fields
22.1 Spectral Representation of Isotropie Correlation Functions and its Consequences
22.2 Examples of Isotropie Correlation Functions
22.3 Spectral Representation of Isotropie Random Fields
22.4 Multidimensional Isotropie Random Fields
22.5 Homogeneous Fields on Spheres and Other Homogeneous Spaces
23. Random Processes with Stationary Increments
24. Generalized Stationary Processes. Processes with Stationary Increments of Order n
24.1 Generalized Random Processes
24.2 A Novel Approach to Processes with Stationary Increments
24.3 Random Processes with Stationary Increments of Order n
25. Generalized Homogeneous Fields. LocaHy Homogeneous and Locally Isotropie Fields
25.1 Generalized Homogeneous Fields
25.2 Locally Homogeneous Fields
25.3 Locally Isotropie Fields
26. Further Examples of Various Spectral Representations
26.1 Karhunen-Loève Expansion
26.2 Moving Average Representations of Stationary Random Processes
26.3 Oscillatory Processes and Evolutionary Spectra
26.4 Harmonizable Random Processes
26.5 Periodically Correlated Processes
26.6 Processes Having Time Average Mean Value and Correlation Function
Bibliography
Index
