概率和鞅

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.

內容概要

　　《概率和鞅》是一部現(xiàn)代概率本科教程，內容生動，敘述嚴格，主要以離散時間的Doob鞅理論為框架，證明了Kolmogorov強大數定理和三級數理論以及通過運用特征函數的中心極限定理這些重要的結果。概率論作為一門應用學科已經廣泛的應用于物理、工程、生物、經濟以及社會科學等眾多領域。

作者簡介

作者：(英國)威廉姆斯 (Williams.D.)

書籍目錄

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

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編輯推薦

《概率和鞅》的最大特點是將概率論講述的清新易懂，通過有選擇性的講述,恰到好處的給出了理解基礎部分的關鍵,一些測度論的重要觀點都在《概率和鞅》的主體部分給出了很好的表述。附錄中給出了有關測度論的完整證明。

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