Probability: Theory and Examples, 5/e (Hardcover)
暫譯: 機率：理論與範例，第5版 (精裝本)
Durrett, Rick
- 出版商: Cambridge
- 出版日期: 2019-05-30
- 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
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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)
這本生動的測度論機率論入門書涵蓋了大數法則、中心極限定理、隨機遊走、馬丁蓋爾、馬可夫鏈、遍歷定理以及布朗運動。專注於對應用最有用的結果，這本全面的著作是一本嚴謹的研究生教材和參考書。根據「學習機率的最佳方式是觀察其運作」的理念，書中包含了延伸的範例，將理論應用於具體的應用場景。這第五版新增了一章關於多維布朗運動及其與偏微分方程（PDEs）之間關係的內容，這是一個正在找到新應用的進階主題。為了奠定這一擴展的基礎，第七章現在包含了伊藤公式的證明。之前僅留給讀者的關鍵練習題現在已直接插入文本中作為引理。新版本重新討論了馬丁蓋爾和穩定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年在史丹佛大學獲得運籌學博士學位。在加州大學洛杉磯分校任教九年後，他在康奈爾大學工作了二十五年，並於2010年轉至杜克大學。他是八本書籍的作者，並在各種主題上發表了超過220篇期刊文章，指導了超過45名博士生。他是美國國家科學院、美國藝術與科學學院的成員，以及數學統計學會和美國數學學會的研究員。
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. 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.
