The Statistical Stability Phenomenon (Mathematical Engineering) - Hardcover

Gorban, Igor I.

Hardcover

ISBN 10: 3319435841 ISBN 13: 9783319435848

Publisher: Springer, 2016

Synopsis

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 this title

About the Author

Igor I. Gorban graduated from the Kiev Polytechnic Institute, USSR,majoring in hydroacoustics. At the MorPhysPribor Central ResearchInstitute, Leningrad, he received a Ph.D., and at the Institute ofCybernetics of the Academy of Sciences of Ukraine, Kiev, a Dr. Sc. Hewas awarded the academic rank of Senior Research Associate and then Full Professor.

He worked at the Kiev Research Institute forHydroequipment, participating in a number of developmental and researchprogrammes. He was in charge of algorithms for several sonar systems,was a research adviser for two scientific expeditions to the Pacific tostudy hydroacoustic signals, was the first deputy to the Chief Designerand Chief Designer of the sonar complexes. 

Since 1993 he hasbeen working at the Institute of Mathematical Machines and SystemsProblems, National academy of Sciences of Ukraine, as PrincipalScientist and Deputy Director for Research. 

Igor I. Gorban is the author of three theories: 

* 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.
Results of his researchs were published in more than 200 scientificpublications, including 12 books, and implemented in the number of sonar systems.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 3319435841
• ISBN 13: 9783319435848
• Binding: Hardcover
• Edition number: 1
• Number of pages: 361