15. The maximum of a martingale

Chapters in this book

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