## STAT 5005: Advanced Probability Theory

• Course Instructor: Qi-Man Shao
• Office: LSB 118
• Office Phone: 3943-7055
• Email: qmshao@cuhk.edu.hk
• Web URL: http://www.sta.cuhk.edu.hk/qmshao
• Time and Venue: 13:30 - 16:15 Thursday, Science Center L4

• Teaching Assistant : GAO Lan
• Office: LSB 130
• Office Phone: 3943-7939
• Office hours: 3:00pm - 5:00pm, Wednesday

• Required Textbook: Probability: Theory and Examples , 4th edition, by Richard Durrett, published by Cambridge University Press.
• Reference Books:
• Probability and Measure , 3rd edition, by Patrick Billingsley
• Probability and Measure Theory by R.B. Ash and C. A. Doleans-Dade
• A Course in Probability Theory , 3rd edition, by Kai Lai Chung

Main topics of this course include: Measure theory, laws of large numbers, Central limit theorems, Random walks and Martingales.

Your course grade is a weighted average of the following performance scores: Homework 20%, Final exam 80%

#### Homework Assignments

• Homework 1 (Due 9/21)
• Homework 2 (Due 10/12):
1.4.1, 1.5.3, 1.5.4, 1.5.6, 1.5.8, 1.5.10, 1.6.2, 1.6.3, 1.6.4, 1.6.6, 1.6.10, 1.6.14, 2.1.4, 2.1.9, 2.1.12
• Homework 3 (Due 10/19):
2.1.15, 2.1.17, 2.2.2, 2.2.3, 2.2.4, 2.2.5, 2.2.6, 2.2.7, 2.2.8, 2.3.2, 2.3.3, 2.3.10, 2.3.11, 2.3.12, 2.3.14, 2.3.15
• Homework 4 (Due 11/2):
2.4.2, 2.4.3, 2.4.4, 2.5.3, 2.5.4, 2.5.5, 2.5.6, 2.5.7, 2.5.9, 2.5.10, 3.1.4, 3.2.2, 3.2.3, 3.2.9, 3.2.11, 3.2.13, 3.2.14, 3.3.10, 3.3.21
• Homework 5 (Due 11/16):
3.4.2, 3.4.4, 3.4.5, 3.4.6, 3.4.7, 3.4.9, 3.4.10, 3.4.11, 3.4.12, 3.4.13, 3.6.8, 3.6.9, 3.6.10, 3.6.11, 3.6.12, 3.9.2, 3.9.7, 3.9.8
• Homework 6 (Due 11/30):
4.1.3, 4.1.5, 4.1.6,4.1.13, 4.1.14, 5.1.5, 5.1.7, 5.1.8, 5.1.9, 5.1.10, 5.1.11, 5.2.4, 5.2.7, 5.2.9, 5.2.11, 5.2.13, 5.3.4