Math/Stat 521: Advanced Probability I

Autumn 2017

Instructor: Zhen-Qing Chen

Phone: (206) 543-1907 (Office)
Fax: (206) 543-0397
Office: Padelford Hall, Room C-341
Office hours: Mondays 1:30-2:20 pm. and Wednesday 2:30-3:20 pm. at Padelford C-341.

Lectures: MWF: 11:30 am.-12:20 pm. at LOW 113.

Textbook: Probability: Theory and Examples by Richard Durrett, Fourth edition, Cambridge University Press, 2010.

Reference Book:
  • K.L. Chung: A Course in Probability Theory, third edition. 2001.

    Course Description

    I plan to cover, approximately, the first five chapters of the textbook in this course. That is:
  • Probability sample spaces, random variables, distribution functions;
  • Expectation and moments;
  • Independence;
  • Weak and strong laws of Large Numbers,
  • Weak convergence, characteristic functions;
  • Central Limit Theorems;
  • Poisson Approximation;
  • Infinitely Divisible and Stable Distributions;
  • Random Walks, stopping times, transience and recurrence.
  • Martingales

    There will be biweekly homework assignments throughout the quarter for your own practice. The most important function of homework is that it helps you to internalize concepts and to develop problem solving skills. There will be two in class exams given on Friday November 3, 2017 and Friday December 8, 2017.
    The home work will count for 20% and the two exams will count for 40% each towards your course grade.

    Prerequisite: Students are assumed to be familiar with measure theory and Lebesgue integration, such as covered in Real Analysis courses Math 524, or Math 426. Chapter 1 and the appendix of the textbook provides a good review of the results from measure theory we needed. You are encouraged to read it for a quick review. You are also supposed to have learned, or learn on your own, some basic combinatorics covered in Math/Stat 394.

    Here is the Course Syllabus pdf format.

    Recommended preparation

    Read the textbook before and after each lecture.

    Homework Assignments