Radically Elementary Probability Theory
1st Edition
Published on 20. June 2016
107 pages
978-1-4008-8214-4 (ISBN)
Description
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.
More details
Other editions
Additional editions
Edward Nelson
Radically Elementary Probability Theory
Book
09/1987
Princeton University Press
€56.70
Shipment within 10-20 days
Edward Nelson
Radically Elementary Probability Theory
Book
09/1987
Princeton University Press
€52.00
Article exhausted; check different version
Person
Edward Nelson
Content
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
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
