出版社：機械工業出版社 ISBN：9787111699170 商品編碼：10047356429700 出版時間：2022-02-07 頁數：436 審圖號：9787111699170 代碼：139 作者：鐘開萊
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商品參數
| 概率論教程（英文版·原書第3版·典藏版） |  | 定價 | 139.00 | | 出版社 | 機械工業出版社 | | 出版時間 | 2022年02月 | | 開本 | 16開 | | 作者 | [美]鐘開萊(Kai Lai Chung) | | 頁數 | 436 | | ISBN編碼 | 9787111699170 |
內容介紹
本書的主要內容如下:隨機變量和分布函數,測度論,數學期望,方差,各種收斂性,大數律, 中心極限定理,特征函數,隨機遊動, 馬氏性和鞅理論.本書內容豐富，邏輯緊密，敘述嚴謹，不僅可以擴展讀者的視野，而且還將為其後續的學習和研究打下堅實基礎。此外，本書的習題較多, 都經過細心的遴選, 從易到難, 便於讀者鞏固練習。本版補充了有關測度和積分方面的內容，並增加了一些習題。
目錄
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 N0te 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 N0te 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 N0te 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 N0te 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 N0te 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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