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Mathematical Engineering

The Statistical Stability Phenomenon

Authors: Gorban, Igor I.

  • For the first time the theory of hyper-random phenomena developed by the author is presented in English, in an extensive and coherent way
  • Broadens our understanding of statistical stability
  • An original contribution to measurement theory
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eBook $139.00
price for USA in USD (gross)
  • ISBN 978-3-319-43585-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
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  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • ISBN 978-3-319-43584-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.99
price for USA in USD
  • ISBN 978-3-319-82863-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

About the authors

Igor I. Gorban graduated from the Kiev Polytechnic Institute, USSR, major-ing in hydroacoustics. At the MorPhysPribor Central Research Institute, Lenin-grad, he received a Ph.D., and at the Institute of Cybernetics of the Academy of Sciences of Ukraine, Kiev, a Dr. Sc. He was awarded the academic rank of Senior Research Associate and then Full Professor.He worked at the Kiev Research Institute for Hydroequipment, participating in a number of developmental and research programmes. He was in charge of algorithms for several sonar systems, was a research adviser for two scientific expeditions to the Pacific to study hydroacoustic signals, was the first deputy to the Chief Designer and Chief Designer of the sonar complexes. Since 1993 he has been working at the Institute of Mathematical Machines and Systems Problems, National academy of Sciences of Ukraine, as Principal Scientist and Deputy Director for Research. Igor I. Gorban is the author of more than 200 scientific publications and several books devoted to: • the theory of space-time processing of hydroacoustic signals under complex dynamic conditions, • the theory of fast multi-channel processing of hydroacoustic signals, and• the physical-mathematical theory of hyper-random phenomena that takes into account violations of statistical stability.

Table of contents (21 chapters)

  • The Phenomenon of Statistical Stability and Its Properties

    Gorban, Igor I.

    Pages 3-22

  • Determinism and Uncertainty

    Gorban, Igor I.

    Pages 23-43

  • Formalization of the Statistical Stability Concept

    Gorban, Igor I.

    Pages 45-54

  • Dependence of the Statistical Stability of a Stochastic Process on Its Spectrum-Correlation Characteristics

    Gorban, Igor I.

    Pages 55-74

  • Experimental Investigation of the Statistical Stability of Physical Processes Over Long Observation Intervals

    Gorban, Igor I.

    Pages 77-90

Buy this book

eBook $139.00
price for USA in USD (gross)
  • ISBN 978-3-319-43585-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • ISBN 978-3-319-43584-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.99
price for USA in USD
  • ISBN 978-3-319-82863-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Statistical Stability Phenomenon
Authors
Series Title
Mathematical Engineering
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-43585-5
DOI
10.1007/978-3-319-43585-5
Hardcover ISBN
978-3-319-43584-8
Softcover ISBN
978-3-319-82863-3
Series ISSN
2192-4732
Edition Number
1
Number of Pages
XXXIX, 322
Number of Illustrations
108 b/w illustrations, 7 illustrations in colour
Additional Information
Originally published by Naukova Dumka Publishing House of National Academy of Sciences of Ukraine, Kiev, 2014
Topics