Radically Elementary Probability Theory. (AM-117), Volume 117 / / Edward Nelson

• Autore: Nelson Edward
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©2016
• Descrizione fisica: 1 online resource (109 pages) : illustrations
• Disciplina: 519.2
• Soggetto topico: Martingales (Mathematics); Stochastic processes; Probabilities
• Soggetto non controllato: Abraham Robinson; Absolute value; Addition; Algebra of random variables; Almost surely; Axiom; Axiomatic system; Borel set; Bounded function; Cantor's diagonal argument; Cardinality; Cartesian product; Central limit theorem; Chebyshev's inequality; Compact space; Contradiction; Convergence of random variables; Corollary; Correlation coefficient; Counterexample; Dimension (vector space); Dimension; Division by zero; Elementary function; Estimation; Existential quantification; Family of sets; Finite set; Hyperplane; Idealization; Independence (probability theory); Indicator function; Infinitesimal; Internal set theory; Joint probability distribution; Law of large numbers; Linear function; Martingale (probability theory); Mathematical induction; Mathematician; Mathematics; Measure (mathematics); N0; Natural number; Non-standard analysis; Norm (mathematics); Orthogonal complement; Parameter; Path space; Predictable process; Probability distribution; Probability measure; Probability space; Probability theory; Probability; Product topology; Projection (linear algebra); Quadratic variation; Random variable; Real number; Requirement; Scientific notation; Sequence; Set (mathematics); Significant figures; Special case; Standard deviation; Statistical mechanics; Stochastic process; Subalgebra; Subset; Summation; Theorem; Theory; Total variation; Transfer principle; Transfinite number; Trigonometric functions; Upper and lower bounds; Variable (mathematics); Variance; Vector space; W0; Wiener process; Without loss of generality
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Frontmatter -- Table of contents -- Preface -- Acknowledgments -- 1. Random variables -- 2. Algebras of random variables -- 3. Stochastic processes -- 4. External concepts -- 5. Infinitesimals -- 6. External analogues of internal notions -- 7. Properties that hold almost everywhere -- 8. L1 random variables 30 -- 9. The decomposition of a stochastic process -- 10. The total variation of a process -- 11. Convergence of martingales -- 12. Fluctuations of martingales -- 13. Discontinuities of martingales -- 14. The Lindeberg condition -- 15. The maximum of a martingale -- 16. The law of large numbers -- 17. Nearly equivalent stochastic processes -- 18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Lévy-Doob-Erdös-Kac-Donsker-Prokhorov theorem -- Appendix -- Index
• Sommario/riassunto: Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
• Titolo autorizzato: Radically Elementary Probability Theory. (AM-117), Volume 117
• ISBN: 1-4008-8214-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154754503321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 117.