| Acknowledgements | 第6-7页 |
| Abstract | 第7页 |
| 0 Introduction | 第8-14页 |
| 1 α-Transience and α-Recurrence of Right Processes | 第14-45页 |
| 1.1 Introduction | 第14-15页 |
| 1.2 α-excessive function | 第15-18页 |
| 1.3 Invariant and absorbing sets | 第18-25页 |
| 1.4 Classification of α-excessive functions | 第25-29页 |
| 1.5 α-Transience and α-Recurrence | 第29-35页 |
| 1.6 α-Recurrence of irreducible processes | 第35-40页 |
| 1.7 α-Excessive measures | 第40-45页 |
| 2 Moment generating functions:quasi-symmetry of probability measures | 第45-59页 |
| 2.1 Basic concepts and results of convex analysis | 第45-48页 |
| 2.2 Moment generating functions of probability measures | 第48-54页 |
| 2.3 Quasi-symmetric probability measures | 第54-59页 |
| 3 Random walks | 第59-76页 |
| 3.1 Ratio limit theorem for random walks on R~n | 第59-66页 |
| 3.2 α-Recurrence of random walks | 第66-72页 |
| 3.3 α-Excessive functions and α-excessive measures of Random walks | 第72-76页 |
| 4 Lévy Processes | 第76-108页 |
| 4.1 Quasi-symmetric Lévy processes | 第76-82页 |
| 4.2 Ratio limit theorems for Lévy process | 第82-85页 |
| 4.3 α-Recurrence of Lévy processes | 第85-96页 |
| 4.4 α-Excessive functions and α-excessive measures for Lévy processes | 第96-100页 |
| 4.5 Symmetrizing measures for Lévy processes | 第100-103页 |
| 4.6 Polynomial recurrence | 第103-108页 |
| BIBLIOGRAPHY | 第108-113页 |
