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定 價:139 元
叢書名:華章數(shù)學原版精品系列
- 作者:[美]鐘開萊(Kai,Lai,Chung)著
- 出版時間:2022/3/1
- ISBN:9787111699170
- 出 版 社:機械工業(yè)出版社
- 中圖法分類:O211
- 頁碼:436
- 紙張:膠版紙
- 版次:1
- 開本:16開
本書的主要內(nèi)容如下:隨機變量和分布函數(shù),測度論,數(shù)學期望,方差,各種收斂性,大數(shù)律, 中心極限定理,特征函數(shù),隨機游動, 馬氏性和鞅理論.本書內(nèi)容豐富,邏輯緊密,敘述嚴謹,不僅可以擴展讀者的視野,而且還將為其后續(xù)的學習和研究打下堅實基礎(chǔ)。此外,本書的習題較多, 都經(jīng)過細心的遴選, 從易到難, 便于讀者鞏固練習。本版補充了有關(guān)測度和積分方面的內(nèi)容,并增加了一些習題。
Kai Lai Chung(鐘開萊,1917-2009) 華裔數(shù)學家、概率學家。1936年考入清華大學物理系,1940年畢業(yè)于西南聯(lián)合大學數(shù)學系,之后任西南聯(lián)合大學數(shù)學系助教。1944年考取第六屆庚子賠款公費留美獎學金。1945年底赴美國留學,1947年獲普林斯頓大學博士學位。20世紀50年代任教于美國紐約州Syracuse大學,60年代以后任斯坦福大學數(shù)學系教授、系主任、名譽教授。鐘開萊著有十余部專著,為世界公認的20世紀后半葉“概率學界學術(shù)教父”。
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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