| 作者 |
| [美]钟开莱(Kai Lai Chung) |
| 丛书名 |
| 华章数学原版精品系列 |
| 出版社 |
| 机械工业出版社 |
| ISBN |
| 9787111699170 |
| 简要 |
| 简介 |
| 内容简介书籍数学书籍 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 |