| Abstract | 第6-7页 |
| Acknowledgements | 第8-12页 |
| 1 Introduction | 第12-18页 |
| 2 Basic Concepts and Results of G-expectations | 第18-37页 |
| 2.1 Preliminaries | 第18-37页 |
| 2.1.1 Completion of a Sublinear Expectation Space | 第23-26页 |
| 2.1.2 G-expectation and G-Brownian Motion | 第26-28页 |
| 2.1.3 Ito ’s Integral of G-Brownian Motion | 第28-30页 |
| 2.1.4 Quadratic Variation Process of G-Brownian Motion | 第30-37页 |
| 3 Upper and Lower Solutions Method for G-SDEs | 第37-58页 |
| 3.0 | 第37-45页 |
| 3.0.5 Upper and Lower Solutions Method | 第38-40页 |
| 3.0.6 Comparison Theorem I | 第40-43页 |
| 3.0.7 G-SDEs with Discontinuous Drift Coefcients | 第43-45页 |
| 3.1 Existence of Solutions for G-SDEs with Discontinuous Second Coef-fcients | 第45-52页 |
| 3.1.1 Comparison Theorem II | 第46-50页 |
| 3.1.2 G-SDEs with Discontinuous Second Coefcients | 第50-52页 |
| 3.2 Existence of Solutions for G-SDEs with Simultaneous Discontinuous First and Second Coefcients | 第52-56页 |
| 3.2.1 Comparison Theorem III | 第53-55页 |
| 3.2.2 G-SDEs with Simultaneous Discontinuous First and Second Coefcients | 第55-56页 |
| 3.3 Discussion | 第56-58页 |
| 4 Existence of Solutions for G-BSDEs | 第58-80页 |
| 4.1 The Method of Upper and Lower Solutions for G-BSDEs | 第59-65页 |
| 4.1.1 Comparison Theorem I for G-BSDEs | 第61-63页 |
| 4.1.2 G-BSDEs with Discontinuous Coefcient f | 第63-65页 |
| 4.2 Existence of Solutions for G-BSDEs with Discontinuous Coefcient h | 第65-72页 |
| 4.2.1 Comparison Theorem II for G-BSDEs | 第67-70页 |
| 4.2.2 G-BSDEs with Discontinuous Coefcient h | 第70-72页 |
| 4.3 G-BSDEs with Simultaneous Discontinuous Coefcients f and h | 第72-78页 |
| 4.3.1 Comparison Theorem III for G-BSDEs | 第73-76页 |
| 4.3.2 G-BSDEs with Discontinuous Coefcients | 第76-78页 |
| 4.4 Discussion | 第78-80页 |
| 5 p-Moment Exponential Stability of G-SDEs | 第80-92页 |
| 5.1 p-Moment Exponential Stability | 第81-86页 |
| 5.1.1 Main Results | 第83-86页 |
| 5.2 Exponential Stability of Linear G-SDEs | 第86-89页 |
| 5.3 q-Moment Instability of G-SDEs | 第89-91页 |
| 5.4 Discussion | 第91-92页 |
| 6 G-SDEs in the Generalized Space | 第92-100页 |
| 6.1 Some Basic Notions | 第92-94页 |
| 6.2 Existence and Uniqueness of G-SDEs in the Generalized Space | 第94-97页 |
| 6.3 Existence and Uniqueness of G-BSDEs in the Generalized Space | 第97-99页 |
| 6.4 Discussion | 第99-100页 |
| 7 Appendix | 第100-102页 |
| References | 第102-111页 |
