高等機率論(博)

The aim of this course is to provide the students with a fairly thorough treatment of the main body of basic and classical probability theory, preceded by an introduction to the mathematics which is necessary for a solid treatment of the material. This means that we begin with basics from measure theory after which we turn to the Borel-Cantelli lemmas, inequalities, transforms, and the two classical limit theorems: the law of large numbers and the central limit theorem. A final chapter on martingales is one of the most efficient, important, and useful tools in probability theory.

None.

(1) Please only download rather than print out the pdf file of the textbook from the website of our university library. (2) The projector and the blackboard will be used in the class.

作業部份: None 考試部份: It is required for every student to present a published paper by June 21, 2019 (i.e., Friday of the 18th week in this semester). The paper should be chosen from "References" of the textbook. The presentation time should be about 30~60 minutes for any undergraduate or master student and about 1~2 hours for any Ph.D. student. Questions and answers are about 15 minutes for any undergraduate or master student and about 30 minutes for any Ph.D. student. 評量部份: (1) Attendance of the class. (2) Presentation of a published paper from "References" of the textbook.

• Chapter 1 Introductory Measure Theory
• Chapter 2 Random Variables
• Chapter 3 Inequalities
• Chapter 4 Characteristic Functions
• Chapter 5 Convergence
• Chapter 6 The Law of Large Numbers
• Chapter 7 The Central Limit Theorem
• Chapter 10 Martingales

Allan Gut (2013). "Probability: A Graduate Course", Second Ed. Springer Science+Business Media, New York.

地點

A416

時間

Every Thursday from 10:10 a.m. to 12:00 p.m.

聯絡方式

(1) E-mail address: cchen@stat.nctu.edu.tw (2) Office phone number: (03) 571-2121 Ext. 31794 or (03) 573-1794