Randomness and Hyper-randomness

  • Igor I. Gorban

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. The Phenomenon of Statistical Stability

    1. Front Matter
      Pages 1-2
  3. Probability Theory

    1. Front Matter
      Pages 25-26
    2. Igor I. Gorban
      Pages 27-50
    3. Igor I. Gorban
      Pages 51-60
  4. Experimental Study of the Statistical Stability Phenomenon

  5. The Theory of Hyper-random Phenomena

  6. The Problem of Adequate Description of the World

    1. Front Matter
      Pages 179-180
  7. Back Matter
    Pages 197-216

About this book


The monograph compares two approaches that describe the statistical stability phenomenon – one proposed by the probability theory that ignores violations of statistical stability and another proposed by the theory of hyper-random phenomena that takes these violations into account. There are five parts. The first describes the phenomenon of statistical stability. The second outlines the mathematical foundations of probability theory. The third develops methods for detecting violations of statistical stability and presents the results of experimental research on actual processes of different physical nature that demonstrate the violations of statistical stability over broad observation intervals. The fourth part outlines the mathematical foundations of the theory of hyper-random phenomena. The fifth part discusses the problem of how to provide an adequate description of the world.
The monograph should be interest to a wide readership: from university students on a first course majoring in physics, engineering, and mathematics to engineers, post-graduate students, and scientists carrying out research on the statistical laws of natural physical phenomena, developing and using statistical methods for high-precision measurement, prediction, and signal processing over broad observation intervals.
To read the book, it is sufficient to be familiar with a standard first university course on mathematics.


Theory of hyper-random phenomena Statistical stability Kolmogorov’s axioms random variable scalar random variable vector random variable hyper-random variable central limit theorem Measurement accuracy random measurement model high precision measurement Wiener—Khinchin transformations Hilbert's sixth problem critical sample size Flicker noise Fractal processes stochastic processes hyper-random processes

Authors and affiliations

  • Igor I. Gorban
    • 1
  1. 1.Institute of Mathematical Machines and Systems ProblemsNational Academy of Sciences of UkraineKievUkraine

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-60779-5
  • Online ISBN 978-3-319-60780-1
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site
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