- 作 者：Emmanuel Lesigne
- 出 版 社：American Mathematical Society
- 出版年份：2005
- ISBN：0821837141
- 标注页数：152 页
- PDF页数：159 页
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Prerequisites and Overview 1
Chapter 1.Modeling a Probabilistic Experiment 3
1.1.Elementary Experiments 3
1.2.Sequences of Elementary Experiments 5
Chapter 2.Random Variables 7
Chapter 3.Independence 11
Chapter 4.The Binomial Distribution 15
Chapter 5.The Weak Law of Large Numbers 19
Chapter 6.The Large Deviations Estimate 23
Chapter 7.The Central Limit Theorem 29
7.1.Statement of the Theorem 29
7.2.Remarks 30
7.3.Applications 33
7.4.Proof of the Theorem 36
Chapter 8.The Moderate Deviations Estimate 45
Chapter 9.The Local Limit Theorem 53
Chapter 10.The Arcsine Law 59
10.1.Introduction 59
10.2.Statement of the Theorems 60
10.3.The Reflection Principle 61
10.4.Proof of the Arcsine Law 66
10.5.Proof of the Law of Returns to the Origin 73
Chapter 11.The Strong Law of Large Numbers 77
11.1.Almost Sure Events, Independent Events 78
11.2.Borel's Strong Law of Large Numbers 82
11.3.Random Sequences Taking Several Values 85
11.4.Normal Numbers 86
11.5.The Borel-Cantelli Lemmas 89
Chapter 12.The Law of the Iterated Logarithm 97
12.1.Introduction 97
12.2.Hausdorff's Estimate 99
12.3.Hardy and Littlewood's Estimate 100
12.4.Khinchin's Law of the Iterated Logarithm 100
Chapter 13.Recurrence of Random Walks 109
13.1.Introduction and Definitions 109
13.2.Nearest Neighbor Random Walks on ZZ 111
13.3.General Results about Random Walks 112
13.4.Recurrence of Random Walks onZN 121
Chapter 14.Epilogue 131
14.1.A Few More General Results 131
14.2.Closing Remarks 135
Biographies 137
Bibliography 147
Index 149