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

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Nelson, Edward,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1988
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 117
• Physical Description: 1 online resource (107 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400882144; 9783110494914; 9783110442496
• DOI: 10.1515/9781400882144
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Edward Nelson.

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.