圖書信息
出版社: 世界圖書出版公司; 第1版 (2010年1月1日)
外文書名: Elementary Probability Theory 4th ed
平裝: 402頁
正文語種: 英語
開本: 24
ISBN: 7510004624, 9787510004629
條形碼: 9787510004629
尺寸: 22.2 x 14.8 x 2 cm
重量: 640 g
內容簡介
《初等機率論(第4版)(英文版)》是一部介紹機率論及其套用的入門教程。其原始版本面世已經有30餘年，但仍然是本科一二年級的經典機率教程。在第4版中增加了兩章講述套用和數學金融。傳承前面版本詳細、嚴謹的風格，講述了有價證券和期貨理論的基本知識。書中用最初等的方法講述了機率測度、隨機變數、分布以及期望等基本概念。離散和連續的案例都有所涉及，在講述後者的時候運用了微積分知識。配以大量的典型例子重點講述機率推理，集中介紹了組合問題、Poison過程、隨機漫步、遺傳模型和Markov鏈。每章末都附有習題及其解答。
目錄
PREFACE TO THE FOURTH EDITION
PROLOGUE TO INTRODUCTION TO MATHEMATICAL FINANCE
1 SET
1.1 Sample sets
1.2 Operations with sets
1.3 Various relations
1.4 Indicator
Exercises
2 PROBABILITY
2.1 Examples of probability
2.2 Definition and illustrations
2.3 Deductions from the axioms
2.4 Independent events
2.5 arithmetical density
Exercises
3 COUNTING
3.1 Fundamental rule
3.2 Diverse ways of sampling
3.3 Allocation models; binomial coefficients
3.4 How to solve it
Exercises
4 RANDOM VARIABLES
4.1 What is a random variable?
4.2 How do random variables come about?
4.3 Distribution and expectation
4.4 Integer-valued random variables
4.5 Random variables with densities
4.6 General case
Exercises
APPENDIX 1: BOREL FIELDS AND GENERAL RANDOM VARIABLES
5 CONDITIONING AND INDEPENDENCE
5.1 Examples of conditioning
5.2 Basic formulas
5.3 Sequential sampling
5.4 P61ya's URN scheme
5.5 Independence and relevance
5.6 Genetical models
Exercises
6 MEAN, VARIANCE, AND TRANSFORMS
6.1 Basic properties of expectation
6.2 The density case
6.3 Multiplication theorem; variance and covariance
6.4 Multinomial distribution
6.5 Generating function and the like
Exercises
7 POISSON AND Normal distributionS
7.1 Models for Poisson distribution
7.2 Poisson process
7.3 From binomial to normal
7.4 Normal distribution
7.5 Central limit theorem
7.6 Law of large numbers
Exercises
APPENDIX 2: STIRLING'S FORMULA AND DE MOIVRE-LAPLACE'S THEOREM
8 FROM Random walks TO MARKOV CHAINS
8.1 Problems of the wanderer or gambler
8.2 Limiting schemes
8.3 Transition probabilities
8.4 Basic structure of Markov chains
8.5 Further developments
8.6 Steady state
8.7 Winding up (or down?)
Exercises
APPENDIX 3: MARTINGALE
9 MEAN-VARIANCE PRICING MODEL
9.1 An investments primer
9.2 Asset return and risk
9.3 Portfolio allocation
9.4 Diversification
9.5 Mean-variance optimization
9.6 Asset return distributions
9.7 Stable probability distributions
Exercises
APPENDIX 4: PARETO AND STABLE LAWS
10 OPTION PRICING THEORY
10.1 Options basics
10.2 Arbitrage-free pricing: 1-period model
10.3 Arbitrage-free pricing: N-period model
10.4 Fundamental asset pricing theorems
Exercises
GENERAL REFERENCES
ANSWERS TO PROBLEMS
VALUES OF THE STANDARD NORMAL DISTRIBUTION FUNCTION
INDEX
