图书介绍
Heads or tails an introduction to limit theorems in probability Emmanuel LesignePDF|Epub|txt|kindle电子书版本网盘下载
- Emmanuel Lesigne 著
- 出版社： American Mathematical Society
- ISBN：0821837141
- 出版时间：2005
- 标注页数：152页
- 文件大小：30MB
- 文件页数：159页
- 主题词：
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图书目录
Prerequisites and Overview1
Chapter 1.Modeling a Probabilistic Experiment3
1.1.Elementary Experiments3
1.2.Sequences of Elementary Experiments5
Chapter 2.Random Variables7
Chapter 3.Independence11
Chapter 4.The Binomial Distribution15
Chapter 5.The Weak Law of Large Numbers19
Chapter 6.The Large Deviations Estimate23
Chapter 7.The Central Limit Theorem29
7.1.Statement of the Theorem29
7.2.Remarks30
7.3.Applications33
7.4.Proof of the Theorem36
Chapter 8.The Moderate Deviations Estimate45
Chapter 9.The Local Limit Theorem53
Chapter 10.The Arcsine Law59
10.1.Introduction59
10.2.Statement of the Theorems60
10.3.The Reflection Principle61
10.4.Proof of the Arcsine Law66
10.5.Proof of the Law of Returns to the Origin73
Chapter 11.The Strong Law of Large Numbers77
11.1.Almost Sure Events, Independent Events78
11.2.Borel's Strong Law of Large Numbers82
11.3.Random Sequences Taking Several Values85
11.4.Normal Numbers86
11.5.The Borel-Cantelli Lemmas89
Chapter 12.The Law of the Iterated Logarithm97
12.1.Introduction97
12.2.Hausdorff's Estimate99
12.3.Hardy and Littlewood's Estimate100
12.4.Khinchin's Law of the Iterated Logarithm100
Chapter 13.Recurrence of Random Walks109
13.1.Introduction and Definitions109
13.2.Nearest Neighbor Random Walks on ZZ111
13.3.General Results about Random Walks112
13.4.Recurrence of Random Walks onZN121
Chapter 14.Epilogue131
14.1.A Few More General Results131
14.2.Closing Remarks135
Biographies137
Bibliography147
Index149