I. Gorban – The Statistical Stability Phenomenon (2017)

Автор: I. Gorban
Название книги: The Statistical Stability Phenomenon
Формат: PDF
Жанр: Математика
Страницы: 349
Качество: Изначально компьютерное, E-book

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 statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability.
The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.
Contents:
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 Investigation of the Statistical Stability of Physical Processes Over Long 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
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
Divergent Sequences and Functions
Description of Divergent Sequences and Functions
Many-Valued Variables, Sequences, and Functions
Principles of the Mathematical Analysis of Many-Valued Functions
The Law of Large Numbers
The Central Limit Theorem
Accuracy and Measurement Models
The Problem of Uncertainty