Radically Elementary Probability Theory

by Edward Nelson

Overview

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.

Product Details

ISBN-13:	9780691084749
Publisher:	Princeton University Press
Publication date:	09/21/1987
Series:	Annals of Mathematics Studies , #117
Pages:	107
Product dimensions:	6.00(w) x 9.10(h) x 0.50(d)

Table of Contents

• Frontmatter, pg. i
• Table of contents, pg. v
• Preface, pg. vii
• Acknowledgments, pg. ix
• 1. Random variables, pg. 1
• 2. Algebras of random variables, pg. 6
• 3. Stochastic processes, pg. 10
• 4. External concepts, pg. 12
• 5. Infinitesimals, pg. 16
• 6. External analogues of internal notions, pg. 20
• 7. Properties that hold almost everywhere, pg. 25
• 8. L1 random variables 30, pg. 30
• 9. The decomposition of a stochastic process, pg. 33
• 10. The total variation of a process, pg. 37
• 11. Convergence of martingales, pg. 41
• 12. Fluctuations of martingales, pg. 48
• 13. Discontinuities of martingales, pg. 53
• 14. The Lindeberg condition, pg. 57
• 15. The maximum of a martingale, pg. 61
• 16. The law of large numbers, pg. 63
• 17. Nearly equivalent stochastic processes, pg. 72
• 18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Lévy-Doob-Erdös-Kac-Donsker-Prokhorov theorem, pg. 75
• Appendix, pg. 80
• Index, pg. 95