概率论：理论与例证（第5版）Probability 5th Edition

基本信息

Series:Cambridge Series in Statistical and Probabilistic Mathematics

Format:Hardback 430 pages, Worked examples or Exercises; 20 Line drawings, black and white

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:5 Revised edition

ISBN:9781108473682

Published:18 Apr 2019

Weight:988g

Dimensions:188 x 261 x 26 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这本关于测量理论概率论的生动介绍涵盖了大数定律、中心极限定理、随机漫步、马丁格、马尔科夫链、遍历定理和布朗运动。本书集中于对应用最有用的结果，是一本严格的研究生教材和参考书。在学习概率的好方法是在行动中看到它的理念下，本书包含将理论应用于具体应用的扩展实例。第五版包含一个关于多维布朗运动及其与偏微分方程（PDEs）关系的新章节，这是一个正在寻找新应用的高级课题。第7章为这一扩展奠定了基础，现在以Itô公式的证明为特色。以前仅仅是留给读者的证明的关键习题，现在直接作为公理插入文本中。

新版重新加入了关于马太效应和静止序列的中心极限定理的讨论。

●提供200个例子和450个问题，使读者能够建立实际的直觉并理解理论的动机。

●提供了一个现代的主题选择，包括多维布朗运动。

●紧凑的风格在完整性和可读性之间取得了平衡，在400页中涵盖了大量的内容。

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 Itô'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.

·Provides 200 examples and 450 problems to equip readers to build practical intuition and understand the motivation for the theory

·Offers a modern selection of topics, including multidimensional Brownian motion

·The compact style strikes a balance between completeness and readability, covering a great deal of ground in 400 pages

作者简介

北卡罗来纳州杜克大学里克-杜瑞特

Rick Durrett是北卡罗来纳州杜克大学数学系的James B. Duke教授。他于1976年在斯坦福大学获得运筹学博士学位。在加州大学洛杉矶分校工作9年和康奈尔大学工作25年后，他于2010年转到杜克大学。他撰写了8本书和220多篇关于各种主题的期刊文章，并指导了45名以上的博士生。他是美国国家科学院和美国艺术与科学学院的成员，也是数学统计研究所和美国数学学会的研究员。

Rick Durrett, Duke University, North Carolina

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.