內容簡介
《機率論教程:英文版(第3版)》是一本享譽世界的經典機率論教材，令眾多讀者受益無窮。自出版以來。已被世界75%以上的大學的數萬名學生使用。《機率論教程:英文版(第3版)》內容豐富，邏輯清晰，敘述嚴謹。不僅可以拓展讀者的視野。而且還將為其後續的學習和研究打下堅實基礎。此外，《機率論教程:英文版(第3版)》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。
作者簡介
KaiLaiChung（鍾開萊，1917-2009）華裔數學家、機率學家。浙江杭州人。1917年生於上海。1936年考入清華大學物理系。1940年畢業於西南聯合大學數學系，之後任西南聯合大學數學系助教。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年代任教於美國紐約州Syracuse大學，60年代以後任史丹福大學數學系教授、系主任、名譽教授。鍾開萊著有十餘部專著。為世界公認的20世紀後半葉“機率學界學術教父”。
目錄
Index
Preface to the third editioniii
Preface to the second editionv
Preface to the first editionvii
1 Distribution function
1.1 Monotone functionsl
1.2 Distribution functions
1.3 Absolutely continuous and singular distributions
2 Measure theory
2.1 Classes of sets
2.2 Probability measures and their distribution functions
3 Random variable. Expectation. Independence
3.1 General definitions
3.2 Properties of mathematical expectation
3.3 Independence
4 Convergence concepts
4.1 Various modes of convergence
4.2 Almost sure convergence; Borel-Cantelli lemma
4.3 Vague convergence
4.4continuation
4.5 Uniform integrability; convergence of moments
5 Law of large numbers. Random series
5.1 Simple limit theorems
5.2 Weak law of large numbers
5.3 Convergence of series
5.4 Strong law of large numbers
5.5 Applications
Bibliographical Note
6 Characteristic function
6.1 General properties; convolutions
6.2 Uniqueness and inversion
6.3 Convergence theorems
6.4 Simple applications
6.5 Representation theorems
6.6 Multidimensional case; Laplace transforms
Bibliographical Note
7 Central limit theorem and its ramifications
7.1 Liapounov's theorem
7.2 Lindeberg-FeUer theorem
7.3 Ramifications of the central limit theorem
7.4 Error estimation
7.5 Law of the iteratedlogarithm
7.6 Infinite divisibility
Bibliographical Note
8 Random walk
8.1 Zero-or-one laws
8.2 Basic notions
8.3 Recurrence
8.4 Fine structure
8.5 Continuation
Bibliographical Note
9 Conditioning. Markov property. Martingale
9.1 Basic properties ofconditionalexpectation3 l
9.2 Conditional independence; Markov property
9.3 Basic properties of smartingales
9.4 Inequalities and convergence
9.5 Applications
Bibliographical Note
Supplement: Measure and Integral
1 Construction of measure
2 Characterization of extensions
3 Measures in R
4 Integral
5 Applications
General Bibliography
