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概率论教程(英文版·原书第3版·典藏版)(概率学界学术教父经典之作)

概率论教程(英文版·原书第3版·典藏版)(概率学界学术教父经典之作)

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2星价¥97.3 定价¥139.0
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  • ISBN:9787111699170
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 开本:16开
  • 页数:419
  • 出版时间:2022-01-01
  • 条形码:9787111699170 ; 978-7-111-69917-0

本书特色

一本享誉世界的经典概率论教材,由概率学界学术教父、华裔数学家钟开莱撰写

内容简介

本书的主要内容如下:随机变量和分布函数,测度论,数学期望,方差,各种收敛性,大数律,中心极限定理,特征函数,随机游动,马氏性和鞅理论。本书内容丰富,逻辑紧密,叙述严谨,不仅可以扩展读者的视野,而且还将为其后续的学习和研究打下坚实基础。此外,本书的习题较多,都经过细心的遴选,从易到难,便于读者巩固练习。本版补充了有关测度和积分方面的内容,并增加了一些习题。

目录

Preface to the third edition iii
Preface to the second edition v
Preface to the first edition vii
1 Distribution function
1.1 Monotone functions 1
1.2 Distribution functions 7
1.3 Absolutely continuous and singular distributions 11
2 Measure theory
2.1 Classes of sets 16
2.2 Probability measures and their distribution function 21
3 Random variable, Expectation.Independence
3.1 General definition 34
3.2 Properties of mathematical expectation 41
3.3 Independence 53
4 Convergence concepts
4.1 Various modes of convergence 68
4.2 Almost sure convergence; Borel-Cantelli lemma 75
4.3 Vague convergence 84
4.4 Continuation 91
4.5 Uniform untegrability; convergence of moments 99
5 Law of large numbers, Randrom series
5.1 Simple limit theorems 106
5.2 Weak low of large nymbers 112
5.3 Convergence of serices 121
5.4 Strong law of large numbers 129
5.5 Applications 138
Bibliographical Note 148
6 Characteristic function
6.1 General properties; convolutions 150
6.2 Uniqueness and inversion 160
6.3 Convergence theorems 169
6.4 Simple applications 175
6.5 Representation theorems 187
6.6 Multidimentstional case; Laplace transforms 196
Bibliographical Note 204
7 Central limit theorem and its ramifications
7.1 Liapounov's theorem 205
7.2 Lindeberg-Feller theorem 214
7.3 Ramifications of the central limit theorem 224
7.4 Error estimation 235
7.5 Law of the iterated logarithm 242
7.6 Infinite divistibility 250
Bibliographical Note 261
8 Random walk
8.1 Zero-or-one laws 263
8.2 Basic notions 270
8.3 Recurrence 278
8.4 Fine structure 288
8.5 Continuation 298
Bibliographical Note 308
9 Conditioning.Markov property. Martingale
9.1 Basic properties of conditional expectation 310
9.2 Conditional independence; Markov propery 322
9.3 Basci properties of smartingales 334
9.4 Inequalities and convergence 346
9.5 Applications 360
Bibliographical Note 373
Supplement: Measure and Integral
1 Construvtion of measure 375
2 Characterization of extensions 380
3 Measures in R 387
4 Integral 395
5 Applications 407
General Bibliography 413
Index 415

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作者简介

Kai Lai Chung(钟开莱,1917-2009) 华裔数学家、概率学家。1936年考入清华大学物理系,1940年毕业于西南联合大学数学系,之后任西南联合大学数学系助教。1944年考取第六届庚子赔款公费留美奖学金。1945年底赴美国留学,1947年获普林斯顿大学博士学位。20世纪50年代任教于美国纽约州Syracuse大学,60年代以后任斯坦福大学数学系教授、系主任、名誉教授。钟开莱著有十余部专著,为世界公认的20世纪后半叶“概率学界学术教父”。

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