05600nam 22015375 450 991015475450332120190708092533.01-4008-8214-110.1515/9781400882144(CKB)3710000000618943(MiAaPQ)EBC4738785(DE-B1597)467948(OCoLC)979911355(DE-B1597)9781400882144(EXLCZ)99371000000061894320190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierRadically Elementary Probability Theory. (AM-117), Volume 117 /Edward NelsonPrinceton, NJ : Princeton University Press, [2016]©20161 online resource (109 pages) illustrationsAnnals of Mathematics Studies ;1200-691-08474-2 0-691-08473-4 Includes bibliographical references and index.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 -- IndexUsing 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.Annals of mathematics studies ;no. 117.Martingales (Mathematics)Stochastic processesProbabilitiesAbraham 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.Martingales (Mathematics)Stochastic processes.Probabilities.519.2Nelson Edward, 346945DE-B1597DE-B1597BOOK9910154754503321Radically Elementary Probability Theory. (AM-117), Volume 1172788042UNINA