Radically Elementary Probability Theory
Published on 21. September 1987
Book
Paperback/Softback
107 pages
978-0-691-08474-9 (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
Series
Language
English
Place of publication
New Jersey
United States
Target group
Professional and scholarly
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 7 mm
Weight
178 gr
ISBN-13
978-0-691-08474-9 (9780691084749)
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Other editions
Additional editions
Edward Nelson
Radically Elementary Probability Theory
E-Book
06/2016
1st Edition
Princeton University Press
€71.49
Available for download
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- Levy-Doob-Erdos-Kac-Donsker-Prokhorov theorem, pg. 75*Appendix, pg. 80*Index, pg. 95