E-Book, Englisch, Band 117, 107 Seiten
Nelson Radically Elementary Probability Theory
1. Auflage 2016
ISBN: 978-1-4008-8214-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 117, 107 Seiten
Reihe: Annals of Mathematics Studies
ISBN: 978-1-4008-8214-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
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
