Randomness and Hyper-randomness

• Main Author: Gorban, Igor I. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Mathematical Engineering,
• Subjects: Applied mathematics.; Engineering mathematics.; Physical measurements.; Measurement .; Statistics .; Probabilities.; Statistical physics.; Signal processing.; Image processing.; Speech processing systems.; 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.

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 par...

Table of Contents:

• Part I The Phenomenon of Statistical Stability
• The Physical Phenomenon of Statistical Stability
• Part II The Probability Theory
• Basis of the Probability Theory
• Stochastic Functions
• Fundamentals of the Mathematical Statistics of the Probability Theory
• Assessment of the Measurement Accuracy on the Basis of Probability Theory
• Part III Experimental Study of the Statistical Stability Phenomenon
• Methodology and Results from Investigation of the Statistical Stability of Processes
• Part IV The Theory of Hyper-Random Phenomena
• Basis of the Theory of Hyper-Random Phenomena
• Hyper-Random Functions
• Fundamentals of the Mathematical Statistics of Hyper-Random Phenomena
• Assessing Measurement Accuracy on the Basis of the Theory of Hyper-Random Phenomena
• Part V The Problem of Adequate Description of the World
• Determinism, Uncertainty, Randomness, And Hyperrandomness
• Epilogue
• References
• Index.