Probability: Theory and Examples, 5/e (Hardcover)

Durrett, Rick

Probability: Theory and Examples, 5/e (Hardcover)
  • 出版商: Cambridge
  • 出版日期: 2019-04-18
  • 定價: $1,480
  • 售價: 9.8 折 $1,450
  • 語言: 英文
  • 頁數: 430
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1108473687
  • ISBN-13: 9781108473682

    • 立即出貨 (庫存=1)

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商品描述

This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications. This fifth edition contains a new chapter on multidimensional Brownian motion and its relationship to partial differential equations (PDEs), an advanced topic that is finding new applications. Setting the foundation for this expansion, Chapter 7 now features a proof of It 's formula. Key exercises that previously were simply proofs left to the reader have been directly inserted into the text as lemmas. The new edition re-instates discussion about the central limit theorem for martingales and stationary sequences.

商品描述(中文翻譯)

這本生動的引論介紹了測度論概率理論的大數定律、中心極限定理、隨機遊走、鞅、馬可夫鏈、遞歸定理和布朗運動。專注於應用最為有用的結果，這本全面的教材是一本嚴謹的研究生教材和參考書。本書的理念是通過實際應用來學習概率，因此包含了將理論應用於具體應用的延伸例子。這本第五版增加了一章關於多維布朗運動及其與偏微分方程（PDEs）的關係，這是一個新的高級主題，正在找到新的應用。為了為這一擴展奠定基礎，第7章現在包含了It 's公式的證明。之前只是留給讀者證明的關鍵練習問題現在直接插入到文本中作為引理。新版重新討論了鞅和平穩序列的中心極限定理。

作者簡介

Rick Durrett is a James B. Duke professor in the mathematics department of Duke University, North Carolina. He received his Ph.D. in Operations Research from Stanford University in 1976. After nine years at University of California, Los Angeles and twenty-five at Cornell University, he moved to Duke University in 2010. He is the author of 8 books and more than 220 journal articles on a wide variety of topics, and has supervised more than 45 Ph.D. students. He is a member of National Academy of Science, American Academy of Arts and Sciences, and a fellow of the Institute of Mathematical Statistics, and of the American Mathematical Society.

作者簡介(中文翻譯)

Rick Durrett是北卡羅來納州杜克大學數學系的詹姆斯·B·杜克教授。他於1976年從斯坦福大學獲得運籌學博士學位。在加州大學洛杉磯分校待了九年，康奈爾大學待了二十五年後，他於2010年轉到杜克大學。他是8本書和超過220篇期刊文章的作者，涵蓋了各種主題，並指導了超過45名博士生。他是美國國家科學院和美國藝術與科學院的成員，也是數理統計學會和美國數學學會的會士。

目錄大綱

1. Measure theory
2. Laws of large numbers
3. Central limit theorems
4. Martingales
5. Markov chains
6. Ergodic theorems
7. Brownian motion
8. Applications to random walk
9. Multidimensional Brownian motion
Appendix. Measure theory details.

目錄大綱(中文翻譯)

1. 測度論
2. 大數定律
3. 中心極限定理
4. 馬丁格爾
5. 馬可夫鏈
6. 遞歸定理
7. 布朗運動
8. 隨機漫步的應用
9. 多維布朗運動
附錄. 測度論細節。

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