概率和鞅

《概率和鞅》是一部现代概率本科教程,内容生动,叙述严格,主要以离散时间的Doob鞅理论为框架,证明了Kolmogorov强大数定理和三级数理论以及通过运用特征函数的中心极限定理这些重要的结果。概率论作为一门应用学科已经广泛的应用于物理、工程、生物、经济以及社会科学等众多领域。

Preface-please read! A Question of Terminology A Guide to Notation Chapter 0 A Branching-Process Example PAPR A: FOUNDATIONS Chapter 1 Measure Spaces Chapter 2 Events Chapter 3 Random Variables Chapter 4 Independence Chapter 5 Integration Chapter 6 Expectation Chapter 7 An Easy Strong Law Chapter 8 Product Measure PART B: MARTINGALE THEORY Chapter 9 Conditional Expectation Chapter 10 Martingales Chapter 11 The Convergence Theorem Chapter 12 Martingales Bounded in Chapter 13 Uniform Integrability Chapter 14 UI Martingales Chapter 15 Applications PART C CHARACTERISTIC FUNCTIONS Chapter 16 Basic Properties of CFs Chapter 17 Weak Convergence Chapter 18 The Central Limit Theorem APPENDICES Chapter A1：Appendix to Chapter 1 Chapter A3：Appendix to Chapter 3 Chapter A4：Appendix to Chapter 4 Chapter A5：Appendix to Chapter 5 Chapter A9：Appendix to Chapter 9 Chapter A13：Appendix to Chapter 13 Chapter A14：Appendix to Chapter 14 Chapter A18：Appendix to Chapter 16 Chapter E: Exercises References Index