概率論教程(英文版原書第3版典藏版)/華章數學原版精品系列
內容大鋼
本書的主要內容如下：隨機變數和分佈函數，測度論，數學期望，方差，各種收斂性，大數律，中心極限定理，特徵函數，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。
作者介紹
(美)鍾開萊|責編:王春華
鍾開萊（1917-2009），浙江杭州人，生於上海，華裔數學家。1936年進入清華大學物理系，1940年畢業於西南聯合大學數學系，之後留校任講師。他先師從華羅庚，後轉投許寶綠（數理統計和概率論領域第一位具有國際聲望的中國數學家）學習概率論。1944年獲得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。二十世紀五十年代任教於美國紐約州雪城（Syracuse）大學，六十年代以後任斯坦福大學數學系教授、系主任、名譽教授。據不完全統計，他直接指導的博士生有15位左右，間接的學術晚輩則超過400位。鍾開萊有十余部著作，其清晰的邏輯和嚴謹的敘述，使得許多教材已經成為享譽世界的經典，影響了幾代學生。
目錄
Preface to the third edition
Preface to the second edition
Preface to the first edition
1 Distribution function
1.1 Monotone functions
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 function
3 Random variable, Expectation.Independence
3.1 General definition
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
4.4 Continuation
4.5 Uniform untegrability; convergence of moments
5 Law of large numbers, Randrom series
5.1 Simple limit theorems
5.2 Weak low of large nymbers
5.3 Convergence of serices
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 Multidimentstional case; Laplace transforms
Bibliographical Note
7 Central limit theorem and its ramifications
7.1 Liapounov's theorem
7.2 Lindeberg-Feller theorem
7.3 Ramifications of the central limit theorem
7.4 Error estimation
7.5 Law of the iterated logarithm
7.6 Infinite divistibility
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 of conditional expectation
9.2 Conditional independence; Markov propery
9.3 Basci properties of smartingales
9.4 Inequalities and convergence
9.5 Applications
Bibliographical Note
Supplement: Measure and Integral
1 Construvtion of measure
2 Characterization of extensions
3 Measures in R
4 Integral
5 Applications
General Bibliography
Index
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