Alan F. Karr 撰写的《概率》

English | PDF | 1993 | 303 Pages | ISBN : 0387940715 | 19.9 MB

This book is a text at the introductory graduate level, for use in the one­ semester or two-quarter probability course for first-year graduate students that seems ubiquitous in departments of statistics, biostatistics, mathemat­ ical sciences, applied mathematics and mathematics. While it is accessi­ ble to advanced ("mathematically mature") undergraduates, it could also serve, with supplementation, for a course on measure-theoretic probability. Students who master this text should be able to read the "hard" books on probability with relative ease, and to proceed to further study in statistics or stochastic processes. This is a book to teach from. It is not encyclopredic, and may not be suitable for all reference purposes. Pascal once apologized to a correspondent for having written a long letter, saying that he hadn't the time to write a short one. I have tried to write a short book, which is quite deliberately incomplete, globally and locally. Many topics, including at least one of everyone's favorites, are omitted, among them, infinite divisibility, interchangeability, large devia­ tions, ergodic theory and the Markov property. These can be supplied at the discretion and taste of instructors and students, or to suit particular interests.

这本书是一本研究生入门级别的教材，适合用一学期或两学期的概率课程使用。这门课程在统计学、生物统计学、数学科学、应用数学和数学系中似乎很普遍。虽然它对高级（有数学背景）的大四本科生是可理解的，但它也可以通过补充材料来用于测度论概率课的教学。读完这本书的学生应该能够相对轻松地阅读“硬核”的概率书籍，并继续深入学习统计学或随机过程。这是一本值得教科书使用的书。它并不全面，也不适合所有的参考目的。帕斯卡曾经为写了一封冗长的信向一位通信者道歉，他说他没有时间写一封简短的信。我试图写一本简短的书，并且故意是不完整的，无论是整体上还是局部上。许多话题都被省略了，包括至少有一个每个人最喜欢的一个，如无限可分性、互换性、大偏差原理、遍历理论和马尔可夫性质。这些可以在教师和学生的选择或满足特定兴趣的情况下补充提供。

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