1.

Record Nr.

UNINA9910154754503321

Autore

Nelson Edward

Titolo

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

Pubbl/distr/stampa

Princeton, NJ : , : Princeton University Press, , [2016]

©2016

ISBN

1-4008-8214-1

Descrizione fisica

1 online resource (109 pages) : illustrations

Collana

Annals of Mathematics Studies ; ; 120

Disciplina

519.2

Soggetti

Martingales (Mathematics)

Stochastic processes

Probabilities

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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.