Knowing the odds : an introduction to probability
著者
書誌事項
Knowing the odds : an introduction to probability
（Graduate studies in mathematics, v. 139）
American Mathematical Society, c2012
大学図書館所蔵 件 / 全39件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
この図書・雑誌をさがす
注記
Includes bibliographical references (p. 413-414) and index
内容説明・目次
内容説明
John Walsh, one of the great masters of the subject, has written a superb book on probability at exactly this level. It covers at a leisurely pace all the important topics that students need to know, and provides excellent examples. I regret his book was not available when I taught such a course myself, a few years ago. --Ioannis Karatzas, Columbia University In this wonderful book, John Walsh presents a panoramic view of Probability Theory, starting from basic facts on mean, median and mode, continuing with an excellent account of Markov chains and martingales, and culminating with Brownian motion. Throughout, the author's personal style is apparent; he manages to combine rigor with an emphasis on the key ideas so the reader never loses sight of the forest by being surrounded by too many trees. As noted in the preface, ``To teach a course with pleasure, one should learn at the same time.'' Indeed, almost all instructors will learn something new from the book, (e.g. the potential-theoretic proof of Skorokhod embedding) and at the same time, it is attractive and approachable for students. --Yuval Peres, Microsoft With many examples in each section that enhance the presentation, this book is a welcome addition to the collection of books that serve the needs of advanced undergraduate as well as first year graduate students. The pace is leisurely which makes it more attractive as a text. --Srinivasa Varadhan, Courant Institute, New York This book covers in a leisurely manner all the standard material that one would want in a full year probability course with a slant towards applications in financial analysis at the graduate or senior undergraduate honors level. It contains a fair amount of measure theory and real analysis built in but it introduces sigma-fields, measure theory, and expectation in an especially elementary and intuitive way. A large variety of examples and exercises in each chapter enrich the presentation in the text.
目次
Preface
Introduction
Chapter 1. Probability spaces
Chapter 2. Random variables
Chapter 3. Expectations II: The general case
Chapter 4. Convergence
Chapter 5. Laws of large numbers
Chapter 6. Convergence in distribution and the CLT
Chapter 7. Markov chains and random walks
Chapter 8. Conditional expectations
Chapter 9. Discrete-parameter martingales
Chapter 10. Brownian motion
Bibliography
Index
「Nielsen BookData」 より