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

✍ Scribed by Edward Nelson

• Publisher: Princeton University Press
• Year: 2016
• Tongue: English
• Leaves: 108
• Series: Annals of Mathematics Studies; 117
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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
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