經典英文數學教材係列：概率和鞅 [Probability with Martingales] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

[英] 威廉姆斯 著

齣版社： 世界圖書齣版公司

ISBN：9787506292511

版次：1

商品編碼：10096490

包裝：平裝

外文名稱：Probability with Martingales

開本：16開

齣版時間：2008-09-01

用紙：膠版紙

頁數：251

正文語種：中文，英語

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，恰到好處的給齣瞭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》的主體部分給齣瞭很好的錶述。附錄中給齣瞭有關測度論的完整證明。

內容簡介

　　《概率和鞅》是一部現代概率本科教程，內容生動，敘述嚴格，主要以離散時間的Doob鞅理論為框架，證明瞭Kolmogorov強大數定理和三級數理論以及通過運用特徵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於物理、工程、生物、經濟以及社會科學等眾多領域。

內頁插圖

目錄

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

前言/序言

　　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.

評分☆☆☆☆☆

好書！沒什麼測度論基礎，讀起來吃力，加油啃?

評分☆☆☆☆☆

性質2（有限可加性）．當n個事件A1，…，An兩兩互不相容時：　P(A1∪。。.∪An)=P(A1)+...+P(An)．

評分☆☆☆☆☆

太快瞭！書很好！

評分☆☆☆☆☆

讀起來有些吃力，英文不過關確實很難讀下去

評分☆☆☆☆☆

好書好書好書好書好書好書好書好書

評分☆☆☆☆☆

統計中有時也用n很大的時候的Fn(A)值當概率的近似值。

評分☆☆☆☆☆

非常經典，幫同學代買的，他很喜歡！

評分☆☆☆☆☆

如果有就稱頻率μn的穩定值p為事件A發生的概率記作P(A)=p[概率的統計定義]

評分☆☆☆☆☆

不可能同時發生的兩個事件叫做互斥事件。