The Statistical Stability Phenomenon

The Statistical Stability Phenomenon by Igor I. Gorban.

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...

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Bibliographic Details
Main Author: Gorban, Igor I. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
Edition:1st ed. 2017.
Series:Mathematical Engineering,
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Physical measurements.
Measurement   .
Statistics .
Statistical physics.
Dynamical systems.
Mathematical physics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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