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

Durrett, Rick

  • 出版商: Cambridge
  • 出版日期: 2019-04-18
  • 售價: $1,480
  • 貴賓價: 9.8$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.

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.

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.