美國康奈爾大學(xué)Rick Durrett教授所著Probability： Theory and Examples一書反映了過去半個多世紀(jì)里概率論與隨機過程的巨大發(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、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。此書選材恰當(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， 為美國多所著名高校選為研究生教材。 此書內(nèi)容包括大數(shù)定律、中心極限定理、隨機游動、鞅論、馬氏鏈、遍歷定理、布朗運動等。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《高等概率論》和《隨機過程論》的教材。 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。注：本書為全英文版。
作者簡介
暫缺《概率論（第3版）》作者簡介
圖書目錄
Introductory Lecture 1 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 Deviations 2 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 ad 3 Random Walks 1. Stopping Times 2. Recurrence 3. Visits to 0, Arcsine Laws 4. Renewal Theory 4 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 Theorems Markov Chains Ergodic Theorems Brownian Motion Appendix:Measure Theory References Notation Normal Table Index
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