出版时间:2008-9 出版社:世界图书出版公司 作者:[英] D. 威廉姆斯 (David Williams) 页数:251
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前言
The most important chapter in this book is Chapter E: Ezercises. I have left the interesting things for you to do. You can start now on the 'EG' exercises, but see 'More about exercises' later in this Preface.The book, which is essentially the set of lecture notes for a third-year undergraduate course at Cambridge, is as lively an introduction as I can manage to the rigorous theory of probability. Since much of the book is devoted to martingales, it is bound to become very lively: look at those Exercises on Chapter 10! But, of course, there is that initial plod through the measure-theoretic foundations. It must be said however that measure theory, that most arid of subjects when done for its own sake, becomes amazingly more alive when used in probability, not only because it is then applied, but also because it is immensely enriched.
内容概要
《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。
作者简介
作者:(英国)威廉姆斯 (Williams.D.)
书籍目录
Preface-please read!A Question of TerminologyA Guide to Notation Chapter 0 A Branching-Process ExamplePAPR 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 MeasurePART 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 ApplicationsPART C CHARACTERISTIC FUNCTIONS Chapter 16 Basic Properties of CFs Chapter 17 Weak Convergence Chapter 18 The Central Limit TheoremAPPENDICES 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 16Chapter E: ExercisesReferencesIndex
章节摘录
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编辑推荐
《概率和鞅》的最大特点是将概率论讲述的清新易懂,通过有选择性的讲述,恰到好处的给出了理解基础部分的关键,一些测度论的重要观点都在《概率和鞅》的主体部分给出了很好的表述。附录中给出了有关测度论的完整证明。
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