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020 _a9783319435855
_9978-3-319-43585-5
024 7 _a10.1007/978-3-319-43585-5
_2doi
050 4 _aTA329-348
050 4 _aTA345-345.5
072 7 _aTBJ
_2bicssc
072 7 _aTEC009000
_2bisacsh
072 7 _aTBJ
_2thema
082 0 4 _a620
_223
100 1 _aGorban, Igor I.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_954194
245 1 4 _aThe Statistical Stability Phenomenon
_h[electronic resource] /
_cby Igor I. Gorban.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXXXIX, 322 p. 115 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematical Engineering,
_x2192-4740
505 0 _aFeatures 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.
520 _aThis 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.
650 0 _aEngineering mathematics.
_93254
650 0 _aEngineering—Data processing.
_931556
650 0 _aMeasurement.
_928731
650 0 _aMeasuring instruments.
_910420
650 0 _aStatistics .
_931616
650 0 _aSystem theory.
_93409
650 0 _aMathematical physics.
_911013
650 1 4 _aMathematical and Computational Engineering Applications.
_931559
650 2 4 _aMeasurement Science and Instrumentation.
_932783
650 2 4 _aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
_931790
650 2 4 _aComplex Systems.
_918136
650 2 4 _aMathematical Physics.
_911013
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_931560
710 2 _aSpringerLink (Online service)
_954195
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319435848
776 0 8 _iPrinted edition:
_z9783319435862
776 0 8 _iPrinted edition:
_z9783319828633
830 0 _aMathematical Engineering,
_x2192-4740
_954196
856 4 0 _uhttps://doi.org/10.1007/978-3-319-43585-5
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c79306
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