The Statistical Stability Phenomenon

Part I. Features of the Phenomenon of Statistical Stability

1. The Phenomenon of Statistical Stability and Its Properties
Igor I. Gorban

2. Determinism and Uncertainty
Igor I. Gorban

3. Formalization of the Statistical Stability Concept
Igor I. Gorban

4. Dependence of the Statistical Stability of a Stochastic Process on Its Spectrum-Correlation Characteristics
Igor I. Gorban

Part II. Experimental Study of the Statistical Stability Phenomenon

5. Experimental Investigation of the Statistical Stability of Physical Processes Over Long Observation Intervals
Igor I. Gorban

6. Experimental Investigation of the Statistical Stability of Meteorological Data
Igor I. Gorban

7. Experimental Studies of the Statistical Stability of Radiation from Astrophysical Objects
Igor I. Gorban

8. Statistical Stability of Different Types of Noise and Process
Igor I. Gorban

Part III. The Theory of Hyper-random Phenomena

9. Hyper-random Events and Variables
Igor I. Gorban

10. Hyper-random Functions
Igor I. Gorban

11. Stationary and Ergodic Hyper-random Functions
Igor I. Gorban

12. Transformations of Hyper-random Variables and Processes
Igor I. Gorban

13. Fundamentals of the Statistics of Hyper-random Phenomena
Igor I. Gorban

Part IV. Principles of the Mathematical Analysis of Divergent and Many-Valued Functions

14. Divergent Sequences and Functions
Igor I. Gorban

15. Description of Divergent Sequences and Functions
Igor I. Gorban

16. Many-Valued Variables, Sequences, and Functions
Igor I. Gorban

17. Principles of the Mathematical Analysis of Many-Valued Functions
Igor I. Gorban

Part V. Statistical Laws in Statistical Stability Violation

18. The Law of Large Numbers
Igor I. Gorban

19. The Central Limit Theorem
Igor I. Gorban

20. Accuracy and Measurement Models
Igor I. Gorban

21. The Problem of Uncertainty
Igor I. Gorban

Keywords: Engineering, Appl.Mathematics/Computational Methods of Engineering, Measurement Science and Instrumentation, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Complex Systems, Mathematical Applications in the Physical Sciences, Statistical Physics and Dynamical Systems