The Statistical Stability Phenomenon

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.

Features of the Statistical Stability Phenomenon.- The Phenomenon of Statistical Stability and its Properties.- Determinism and Uncertainty.- Formalization of the Statistical Stability Concept.- Dependence of the Statistical Stability of a Stochastic Process on its Spectrum-Correlation Characteristics.- Experimental Study of the Statistical Stability Phenomenon.- Experimental Investigation of the Statistical Stability of Physical Processes over Large Observation Intervals.- Experimental Investigation of the Statistical Stability of Meteorological Data.- Experimental Studies of the Statistical Stability of Radiation from Astrophysical Objects.- Statistical Stability of Different Types of Noise and Process.- The Theory of Hyper-random Phenomena.- Hyper-random Events and Variables.- Hyper-random Functions.- Stationary and Ergodic Hyper-random Functions.- Transformations of Hyper-random Variables and Processes.- Fundamentals of the Statistics of Hyper-random Phenomena.- Principles of the Mathematical Analysis of Divergent and Many-valued Functions.- Divergent Sequences and Functions.- Description of Divergent Sequences and Functions.- Divergent Sequences.- Many-valued Variables, Sequences, and Functions.- Principles of the Mathematical Analysis of Many-valued Functions.- Statistical Laws in Statistical Stability Violation.- The Law of Large Numbers.- The Central Limit Theorem.- Accuracy and Measurement Models.- The Problem of Uncertainty.- Epilogue.- References.