Radically Elementary Probability Theory. (AM-117), Volume 117 / / 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 conven...
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Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1988 |
Year of Publication: | 2016 |
Language: | English |
Series: | Annals of Mathematics Studies ;
117 |
Online Access: | |
Physical Description: | 1 online resource (107 p.) |
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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 |
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Summary: | 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. |
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. |