Statistical Stability Phenomenon

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.

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• Probabilidade e Estatística
• Física Matemática
• Matemática para engenheiros
• Mensuração e sistemas de medição
• Cibernética e teoria dos sistemas

sixth Hilbert's problem;Wiener-Khinchin transformation;Flicker noise;hyper-random phenomena;hyper-random events;hyper-random variable;hyper-random functions;statistical stability violation;central limit theorem