The Statistical Stability Phenomenon

• Main Author: Gorban, Igor I. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Mathematical Engineering,
• Subjects: Engineering.; System theory.; Mathematical physics.; Physical measurements.; Measurement.; Statistics.; Applied mathematics.; Engineering mathematics.; 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.

This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations – the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of s...

Table of Contents:

• Features of the Statistical Stability Phenomenon
• The Phenomenon of Statistical Stability and its Properties
• Determinism and Uncertainty
• Formalization of the Statistical Stability Concept
• Dependence of the Statistical Stability of a Stochastic Process on its Spectrum-Correlation Characteristics
• Experimental Study of the Statistical Stability Phenomenon
• Experimental Investigation of the Statistical Stability of Physical Processes over Large Observation Intervals
• Experimental Investigation of the Statistical Stability of Meteorological Data
• Experimental Studies of the Statistical Stability of Radiation from Astrophysical Objects
• Statistical Stability of Different Types of Noise and Process
• The Theory of Hyper-random Phenomena
• Hyper-random Events and Variables
• Hyper-random Functions
• Stationary and Ergodic Hyper-random Functions
• Transformations of Hyper-random Variables and Processes
• Fundamentals of the Statistics of Hyper-random Phenomena
• Principles of the Mathematical Analysis of Divergent and Many-valued Functions
• Divergent Sequences and Functions
• Description of Divergent Sequences and Functions
• Divergent Sequences
• Many-valued Variables, Sequences, and Functions
• Principles of the Mathematical Analysis of Many-valued Functions
• Statistical Laws in Statistical Stability Violation
• The Law of Large Numbers
• The Central Limit Theorem
• Accuracy and Measurement Models
• The Problem of Uncertainty
• Epilogue
• References.