Probability essentials概率原理
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作者： Jean Jacod，Philip Protter著
出 版 社： 湖南文艺出版社
出版时间： 2004-8-1字数：版次： 1页数： 254印刷时间： 2004/08/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540438717包装： 平装内容简介
“（The book is） a lean and largely self-contained introduction to the modern theory of probability，aimed at advanced undergraduate or beginning graduate students。 The 28 short chapters belie the book’s genesis as polished lecture notes；the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises，The authors make it clear what luggage is required for this exhilarating trek，a good knowledge of advanced calculus，some linear algebra，and some "mathematical sophistication”。 With this understood，the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery。 Within the constraints of a slim volume，it is hard to imagine how the authors could have done a more effective or more attractive job。“The Mathematical Gazette，Vol。 84，No 500，2000 "The authors provide the shortest path through the twenty-eight chapter headings。 The topics are treated in a mathematically and pedagogically digestible way。 The writing is concise and crisp： the average chapter length is about eight pages，Numerous exercises add to the value of the text as a teaching tool。 In conclusion，this is an excellent text for the intended audience。”
目录
1 Introduction
2 Axioms of Probability
3 Conditional Probability and Independence
4 Probabilities on a Finite or Countable Space
5 Random Variables on a Countable Space
6 Construction of a Probability Measure
7 Construction of a Probability Measure on R
8 Random Variables
9 Integration with Respect to a Probability Measure
10 Independent Random Variables
11 Probability Distributions on R
12 Probability Distributions on Rn
13 Characteristic Functions
14 Properties of Characteristic Functions
15 Sums of Independent Random Variables
16 Gaussian Random Variables The Normal and the Multivariate Normal Distributions
17 Convergence of Random Variables
18 Weak Convergence
19 Weak Convergence and Characteristic Functions
20 The Laws of Large Numbers
21 The Central Limit Theorem
22 L and Hilbert Spaces
23 Conditional Expectation
24 Martingales
25 Supermartingales and Submartingales
26 Martingale Inequalities
27 Martingale Convergence Theorems
28 The Radon-Nikodym Theorem
References
Index
