Overview
- Critically reviews and compares the most established probability theory with the more recent theory of hyper-random phenomena
- Broadens our understanding of statistical stability
- Written by the father of the theory of hyper-random phenomena
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Engineering (MATHENGIN)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (11 chapters)
-
Front Matter
-
The Phenomenon of Statistical Stability
-
Front Matter
-
-
Experimental Study of the Statistical Stability Phenomenon
-
Front Matter
-
-
The Problem of Adequate Description of the World
-
Front Matter
-
-
Back Matter
Keywords
- 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
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.
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Randomness and Hyper-randomness
Authors: Igor I. Gorban
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-319-60780-1
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-60779-5Published: 08 September 2017
Softcover ISBN: 978-3-319-86931-5Published: 11 August 2018
eBook ISBN: 978-3-319-60780-1Published: 31 August 2017
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XXXII, 216
Number of Illustrations: 7 b/w illustrations, 23 illustrations in colour
Topics: Mathematical and Computational Engineering, Measurement Science and Instrumentation, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Probability Theory and Stochastic Processes, Statistical Physics and Dynamical Systems, Signal, Image and Speech Processing