The Statistical Stability Phenomenon

  • Igor I. Gorban

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xxxix
  2. Features of the Phenomenon of Statistical Stability

  3. Experimental Study of the Statistical Stability Phenomenon

  4. The Theory of Hyper-random Phenomena

    1. Front Matter
      Pages 119-120
    2. Igor I. Gorban
      Pages 121-142
    3. Igor I. Gorban
      Pages 143-158
    4. Igor I. Gorban
      Pages 159-175
  5. Principles of the Mathematical Analysis of Divergent and Many-Valued Functions

    1. Front Matter
      Pages 205-205
    2. Igor I. Gorban
      Pages 207-214
  6. Statistical Laws in Statistical Stability Violation

    1. Front Matter
      Pages 245-245
    2. Igor I. Gorban
      Pages 247-259
    3. Igor I. Gorban
      Pages 261-270
    4. Igor I. Gorban
      Pages 271-296
    5. Igor I. Gorban
      Pages 297-309
  7. Back Matter
    Pages 311-322

About this 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.


sixth Hilbert’s problem Wiener-Khinchin transformation Flicker noise hyper-random phenomena hyper-random events hyper-random variable hyper-random functions statistical stability violation central limit theorem

Authors and affiliations

  • Igor I. Gorban
    • 1
  1. 1.National Academy of Sciences of UkraineInstitute of Mathematical Machines and Systems ProblemKievUkraine

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-43584-8
  • Online ISBN 978-3-319-43585-5
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
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