| English Abstract | 第1-15页 |
| Chinese Abstract | 第15-23页 |
| Chapter 1 Laws of large numbers of negatively correlated random variables for capacities | 第23-50页 |
| §1.1 Introduction | 第23-25页 |
| §1.2 Preliminaries | 第25-29页 |
| §1.3 Examples of capacities | 第29-33页 |
| §1.4 Laws of large numbers for upper probabilities | 第33-40页 |
| §1.5 Laws of large numbers for 2-alternating capacities | 第40-50页 |
| Chapter 2 Some properties of g-probabilities induced by BSDEs | 第50-93页 |
| §2.1 Introduction | 第50-53页 |
| §2.2 g-probability and 2-alternating capacity | 第53-57页 |
| §2.3 Some inequalities for g-probability | 第57-62页 |
| §2.4 Laws of large numbers for g-probablities | 第62-76页 |
| §2.4.1 Hypothese and notations | 第62-66页 |
| §2.4.2 Laws of large numbers in a broad sense | 第66-72页 |
| §2.4.3 Examples | 第72-75页 |
| §2.4.4 A weak law of large numbers by Chebyshev inequality | 第75-76页 |
| §2.5 Correlation of random variables under g-expectation | 第76-93页 |
| §2.5.1 Preliminaries | 第76-81页 |
| §2.5.2 Variance of a random variable | 第81-83页 |
| §2.5.3 Correlation of random variables | 第83-89页 |
| §2.5.4 Correlation coefficient of random variables | 第89-93页 |
| Chapter 3 Variational formula via BSDEs | 第93-102页 |
| §3.1 Introduction | 第93-94页 |
| §3.2 Preliminaries | 第94-96页 |
| §3.3 An extended variational formula via BSDEs | 第96-100页 |
| §3.4 Results in canonical space proved by means of BSDEs | 第100-102页 |
| Reference | 第102-110页 |
| The Completed Papers | 第110-111页 |
| Acknowledgement | 第111-112页 |
| 学位论文评阅及答辩情况表 | 第112-216页 |
