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概率论入门 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （美）雷斯尼克（ResnickS.I.）著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510058271
- 出版时间：2013
- 标注页数：453页
- 文件大小：42MB
- 文件页数：464页
- 主题词：概率论－教材－英文
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图书目录
1 Sets and Events1
1.1 Introduction1
1.2 Basic Set Theory2
1.2.1 Indicator functions5
1.3 Limits of Sets6
1.4 Monotone Sequences8
1.5 Set Operations and Closure11
1.5.1 Examples13
1.6 Theσ-field Generated by a Given Class C15
1.7 Borel Sets on the Real Line16
1.8 Comparing Borel Sets18
1.9 Exercises20
2 Probability Spaces29
2.1 Basic Definitions and Properties29
2.2 More on Closure35
2.2.1 Dynkin's theorem36
2.2.2 Proof of Dynkin's theorem38
2.3 Two Constructions40
2.4 Constructions of Probability Spaces42
2.4.1 General Construction of a Probability Model43
2.4.2 Proof of the Second Extension Theorem49
2.5 Measure Constructions57
2.5.1 Lebesgue Measure on(0,1]57
2.5.2 Construction of a Probability Measure on R witl Given Distribution Function F(x)61
2.6 Exercises63
3 Random Variables,Elements,and Measurable Maps71
3.1 Inverse Maps71
3.2 Measurable Maps,Random Elements,Induced Probability Measures74
3.2.1 Composition77
3.2.2 Random Elements of Metric Spaces78
3.2.3 Measurability and Continuity80
3.2.4 Measurability and Limits81
3.3 σ-Fields Generated by Maps83
3.4 Exercises85
4 Independence91
4.1 Basic Definitions91
4.2 Independent Random Variables93
4.3 Two Examples of Independence95
4.3.1 Records,Ranks,Renyi Theorem95
4.3.2 Dyadic Expansions of Uniform Random Numbers98
4.4 More on Independence：Groupings100
4.5 Independence,Zero-One Laws,Borel-Cantelli Lemma102
4.5.1 Borel-Cantelli Lemma102
4.5.2 Borel Zero-One Law103
4.5.3 Kolmogorov Zero-One Law107
4.6 Exercises110
5 Integration and Expectation117
5.1 Preparation for Integration117
5.1.1 Simple Functions117
5.1.2 Measurability and Simple Functions118
5.2 Expectation and Integration119
5.2.1 Expectation of Simple Functions119
5.2.2 Extension of the Definition122
5.2.3 Basic Properties of Expectation123
5.3 Limits and Integrals131
5.4 Indefinite Integrals134
5.5 The Trarnsformation Theorem and Densities135
5.5.1 Expectation is Always an Integral on R137
5.5.2 Densities139
5.6 The Riemann vs Lebesgue Integral139
5.7 Product Spaces143
5.8 Probability Measures on Product Spaces147
5.9 Fubini's theorem149
5.10 Exercises155
6 Convergence Concepts167
6.1 Almost Sure Convergence167
6.2 Convergence in Probability169
6.2.1 Statistical Terminology170
6.3 Connections Between a.s.and i.p.Convergence171
6.4 Quantile Estimation178
6.5 Lp Convergence180
6.5.1 Uniform Integrability182
6.5.2 Interlude：A Review of Inequalities186
6.6 More on Lp Convergence189
6.7 Exercises195
7 Laws of Large Numbers and Sums of Independent Raudom Variables203
7.1 Truncation and Equivalence203
7.2 A General Weak Law of Large Numbers204
7.3 Almost Sure Convergence of Sums of Independent Random Variables209
7.4 Strong Laws of Large Numbers213
7.4.1 Two Examples215
7.5 The Strong Law of Large Numbers for IID Sequences219
7.5.1 Two Applications of the SLLN222
7.6 The Kolmogorov Three Series Theorem226
7.6.1 Necessity of the Kolmogorov Three Series Theorem230
7.7 Exercises234
8 Convergence in Distribution247
8.1 Basic Definitions247
8.2 Scheffé's lemma252
8.2.1 Scheffé's lemma and Order Statistics255
8.3 The Baby Skorohod Theorem258
8.3.1 The Delta Method261
8.4 Weak Convergence Equivalences；Portmanteau Theorem263
8.5 More Relations Among Modes of Convergence267
8.6 New Convergences from Old268
8.6.1 Example：The Central Limit Theorem for m-Dependent Random Variables270
8.7 The Convergence to Types Theorem274
8.7.1 Application of Convergence to Types：Limit Distributions for Extremes278
8.8 Exercises282
9 Characteristic Functions and the Central Limit Theorem293
9.1 Review of Moment Generating Functions and the Central Limit Theorem294
9.2 Characteristic Functions：Definition and First Properties295
9.3 Expansions297
9.3.1 Expansion of eix297
9.4 Moments and Derivatives301
9.5 Two Big Theorems：Uniqueness and Continuity302
9.6 The Selection Theorem,Tightness,and Prohorov's theorem307
9.6.1 The Selection Theorem307
9.6.2 Tightness,Relative Compactness,and Prohorov's theorem309
9.6.3 Proof of the Continuity Theorem311
9.7 The Classical CLT for iid Random Variables312
9.8 The Lindeberg-Feller CLT314
9.9 Exercises321
10 Martingales333
10.1 Prelude to Conditional Expectation：The Radon-Nikodym Theorem333
10.2 Definition of Conditional Expectation339
10.3 Properties of Conditional Expectation344
10.4 Martingales353
10.5 Examples of Martingales356
10.6 Connections between Martingales and Submartingales360
10.6.1 Doob's Decomposition360
10.7 Stopping Tirmes363
10.8 Positive Super Martingales366
10.8.1 Operations on Supermartingales367
10.8.2 Uperossings369
10.8.3 Boundedness Properties369
10.8.4 Convergence of Positive Super Martingales371
10.8.5 Closure374
10.8.6 Stopping Supermartingales377
10.9 Examples379
10.9.1 Gambler's Ruin379
10.9.2 Branching Processes380
10.9.3 Some Differentiation Theory382
10.10 Martingale and Submartingale Convergence386
10.10.1 Krickeberg Decomposition386
10.10.2 Doob's(Sub)martingale Convergence Theorem387
10.11 Regularity and Closure388
10.12 Regularity and Stopping390
10.13 Stopping Theorems392
10.14 Wald's Identity and Random Walks398
10.14.1 The Basic Martingales400
10.14.2 Regular Stopping Times402
10.14.3 Examples of Integrable Stopping Times407
10.14.4 The Simple Random Walk409
10.15 Reversed Martingales412
10.16 Fundamental Theorems of Mathematical Finance416
10.16.1 A Simple Market Model416
10.16.2 Admissible Strategies and Arbitrage419
10.16.3 Arbitrage and Martingales420
10.16.4 Complete Markets425
10.16.5 Option Pricing428
10.17 Exercises429
References443
Index445