概率論

內(nèi)容概要

本書由美國康奈爾大學(xué)Rick Durrett教授撰寫，書中反映了過去半個多世紀(jì)概率論與隨機(jī)過程的巨大發(fā)展，體現(xiàn)了概率論與其他學(xué)科深刻聯(lián)系以及在工程、經(jīng)濟(jì)、金融等方面的應(yīng)用，繼承了美國在概率論教育實踐中所積累的經(jīng)驗。本書選材恰當(dāng)，編排合理，難度適中，兼顧理論與應(yīng)用，契合當(dāng)今研究生教學(xué)的實際情況，被美國多所著名高校選為研究生教材。    本書內(nèi)容包括大數(shù)定律、中心極限定理、隨機(jī)游動、鞅論、馬氏鏈、遍歷定理、布朗運(yùn)動等。附錄部分收錄了所需的測度論知識。此書宜為概率統(tǒng)計專業(yè)研究生教材。對于學(xué)過概率論的學(xué)者而言，這也不失為一本出色的參考書。

作者簡介

作者：(美)杜雷特

書籍目錄

Introductory Lecture1 Laws of Large Numbers  1. Basic Definitions  2. Random Variables  3. Expected Value    a. Inequalities    b. Integration to the limit    c. Computing expected values  4. Independence    a. Sufficient conditions for independence    b. Independence, distribution, and expectation    c. Constructing independent random variables  5. Weak Laws of Large Numbers    a. L2 weak laws    b. Triangular arrays    c. Truncation  6. Borel-Cantelli Lemmas  7. Strong Law of Large Numbers  8. Convergence of Random Series  9. Large Deviations2 Central Limit Theorems  1. The De Moivre-Laplace Theorem  2. Weak Convergence    a. Examples    b. Theory  3. Characteristic Functions    a. Definition, inversion formula    b. Weak convergence    c. Moments and derivatives    d. Polya's criterion    e. The moment problem  4. Central Limit Theorems    a. i.i.d, sequences    b. Triangular arrays    c. Prime divisors (Erd0s-Kac)    d. Rates of convergence (Berry-Esseen)  5. Local Limit Theorems  6. Poisson Convergence    a. Basic limit theorem    b. Two examples with dependence    c. Poisson processes  7. Stable Laws  8. Infinitely Divisible Distributions  9. Limit theorems in ad3 Random Walks  1. Stopping Times  2. Recurrence  3. Visits to 0, Arcsine Laws  4. Renewal Theory4 Martingales  1. Conditional Expectation    a. Examples    b. Properties    c. Regular conditional probabilities  2. Martingales, Almost Sure Convergence  3. Examples  236    a. Bounded increments    b. Polya's urn scheme    c. Radon-Nikodym derivatives    d. Branching processes  4. Doob's Inequality, Lp Convergence Square integrable martingales  5. Uniform Integrability, Convergence in L1  6. Backwards Martingales  7. Optional Stopping TheoremsMarkov ChainsErgodic TheoremsBrownian MotionAppendix:Measure TheoryReferencesNotationNormal TableIndex

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