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Record Nr. |
UNINA9910154754503321 |
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Autore |
Nelson Edward |
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Titolo |
Radically Elementary Probability Theory. (AM-117), Volume 117 / / Edward Nelson |
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Pubbl/distr/stampa |
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Princeton, NJ : , : Princeton University Press, , [2016] |
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©2016 |
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ISBN |
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Descrizione fisica |
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1 online resource (109 pages) : illustrations |
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Collana |
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Annals of Mathematics Studies ; ; 120 |
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Disciplina |
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Soggetti |
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Martingales (Mathematics) |
Stochastic processes |
Probabilities |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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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Sommario/riassunto |
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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. |
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