Probabilities and Potential, B

Front Cover 2
Probabilities and Potential B: Theory of Martingales 5
Copyright Page 6
Contents 9
Complements to Chapter IV: Some useful properties of jumps of cadlag processes 15
CHAPTER V. GENERALITIES AND THE DISCRETE CASE 21
- 1. Definitions and general properties 21
- 2. Doob's stopping theorem 26
- 3. Fundamental inequalities 33
- 4. Convergence and decomposition theorems 41
- 5. Some applications of the convergence theorems 58
CHAPTER VI. CONTINUOUS PARAMETER MARTINGALES 85
- 1. Right continuous supermartingales 86
- 2. Projections and dual projections 123
- 3. Increasing processes and potentials 169

Front Cover 2
Probabilities and Potential B: Theory of Martingales 5
Copyright Page 6
Contents 9
Complements to Chapter IV: Some useful properties of jumps of cadlag processes 15
CHAPTER V. GENERALITIES AND THE DISCRETE CASE 21
- 1. Definitions and general properties 21
- 2. Doob's stopping theorem 26
- 3. Fundamental inequalities 33
- 4. Convergence and decomposition theorems 41
- 5. Some applications of the convergence theorems 58
CHAPTER VI. CONTINUOUS PARAMETER MARTINGALES 85
- 1. Right continuous supermartingales 86
- 2. Projections and dual projections 123
- 3. Increasing processes and potentials 169
CHAPTER VII. DECOMPOSITION OF SUPERMARTINGALES, APPLICATIONS 203
- 1. The decomposition theorem 203
- 2. Definition and first properties of semimartingales 232
- 3. Hp spaces of martingales and semimartigales 272
CHAPTER VIII. STOCHASTIC INTEGRALS, STRUCTURE OF MARTINGALES 329
- 1. Stochastic integral of locally bounded predictable processes 329
- 2. Structure of martingales and local martingales 359
- 3. Two extensions of the notion of astochastic intergal 397
- 4. A characterization of semimartingales 406
APPENDIX 1: STRONG SUPERMARTINGALES 413
APPENDIX 2: COMPLEMENTS ON QUASIMARTINGALES 441
COMMENTS 447
BIBLIOGRAPHY 455
INDEX 475
INDEX OF NOTATION 481

Theory of Martingales