Randomness and hyper-randomness. (©2018)

• Record Type: Book
• Further Information: Note: Igor I. Gorban.
• Other Names: Gorban, I. I (Igor I.), 1952-
• Contents: Preface; References; Acknowledgments; References; Introduction; References; Contents; About the Author; Symbols; Part I: The Phenomenon of Statistical Stability; References; Chapter 1: The Physical Phenomenon of Statistical Stability; 1.1 Manifestation of the Phenomenon of Statistical Stability; 1.1.1 Statistical Stability of the Relative Frequency of Events; 1.1.2 Statistical Stability of Statistics; 1.2 Interpretations of the Phenomenon of Statistical Stability; 1.2.1 Perfect Statistical Stability; 1.2.2 Imperfect Statistical Stability. 1.3 Identical and Statistically Unpredictable Conditions1.4 Hilbertś Sixth Problem; 1.4.1 The Essence of the Problem; 1.4.2 Approaches to Axiomatizing Probability Theory; 1.4.3 How to Solve Hilbertś Sixth Problem; 1.5 Adequacy Axioms; 1.5.1 Description of the Phenomenon of Statistical Stability in the Framework of Probability Theory; 1.5.2 Description of the Phenomenon of Statistical Stability in the Framework of the Theory of Hyper-random Phenomena; 1.6 Is Probability a `Normal ́Physical Quantity?; References; Part II: Probability Theory; References; Chapter 2: Basis of Probability Theory. 2.1 The Concept of Random Phenomena2.2 Options for the Definition of Probability; 2.2.1 Classical Approach; 2.2.2 Statistical Approach; 2.2.3 Main Concepts of Set Theory; 2.2.4 Main Concepts of Measure Theory; 2.2.5 Axiomatic Definition of Probability; 2.2.6 Random Events; 2.3 Random Variables; 2.3.1 Basic Definitions; 2.3.2 Probabilistic Characteristics of a Scalar Random Variable; 2.3.3 Probabilistic Characteristics of a Discrete Random Variable; 2.3.4 Examples of Random Variables; 2.3.5 Numerical Parameters of Scalar Random Variables; 2.3.6 Numerical Parameters of Various Random Variables. 2.4 Vector Random Variables2.4.1 Probabilistic Characteristics of a System of Two Random Variables; 2.4.2 Numerical Parameters of a System of Two Random Variables; 2.4.3 System of Two Jointly Gaussian Random Variables; 2.4.4 Characteristics and Parameters of a System of more than Two Random Variables; 2.5 Operations on Random Variables; References; Chapter 3: Stochastic Functions; 3.1 Main Concepts; 3.2 Description of Stochastic Processes; 3.3 Gaussian Stochastic Process; 3.4 Stationary Stochastic Processes; 3.4.1 Stochastic Processes That Are Stationary in the Narrow Sense. 3.4.2 Stochastic Processes That Are Stationary in the Broad Sense3.5 Spectral Description of Stochastic Processes; 3.5.1 Wiener-Khinchin Transformation; 3.5.2 Narrowband and Broadband Processes; 3.5.3 Generalized Wiener-Khinchin Transformation; 3.6 Ergodic Stochastic Processes; 3.7 Transformation of Stochastic Processes; References; Chapter 4: Fundamentals of the Mathematical Statistics of Probability Theory; 4.1 Statistics of Random Variables; 4.1.1 A Random Sample; 4.1.2 Assessments of Probability Characteristics; 4.1.3 Assessment of Moments; 4.2 Convergence of Sequences of Random Variables.
• Publisher Details: Cham : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource (240 pages)
• Subjects: 519.2; Engineering; Probabilities; Random variables; MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General; Probabilities; Random variables; Science -- Weights & Measures; Mathematics -- Probability & Statistics -- General; Science -- Mathematical Physics; Technology & Engineering -- Electronics -- General; Mensuration & systems of measurement; Probability & statistics; Statistical physics; Imaging systems & technology; Engineering mathematics; Statistics; Distribution (Probability theory); Statistical physics; Mathematics -- Applied; Maths for engineers; Electronic books
• Languages: English
• ISBNs: 9783319607801; 3319607804
• Related ISBNs: 9783319607795; 3319607790
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.