MATH280B Probability Theory II, Winter 2018

Instructor:

Tianyi Zheng (tzheng2@math.ucsd.edu)

Lectures:

3:00-3:50PM on Mondays, Wednesdays, and Fridays in AP&M 5402. 

Office Hours:

Tianyi: Mondays and Wednesdays 4-5:30pm in AP&M 6202.

Grading:

Homework will count for 60% for the letter grade.

There will be a take home final exam, which will count for 40% for the letter grade.

Textbook & References:

Recommended textbook: Probability: Theory and Examples by Rick Durrett, here is a link to the electronic copy of the book.

Alternative reference: A Probability Path by Sidney Resnick, here is a link to the electronic copy of the book.

Homework assignment:

There are 3 homework problem sets through the quarter.

First homework HW1, due Jan 26 2018.

Second homework HW2, due on Feb 16 2018.

Third homework HW3, due on Mar 9 2018.

Solution sketches: solution.

Material covered in 280B:

We will cover roughly Chapter 3 and Chapter 5 in the textbook by Durrett, if time permits we will cover part of Chapter 7 in Durrett’s book. Main topics are:

1. Convergence in distribution, central limit theorems.

2. Conditional expectation. Martingales.

3. Basic ergodic theorems.