Syllabus for Math 564

Syllabus for Math 564, Fall 2009

Instructor: Bartlomiej Siudeja, siudeja@illinois.edu
Class meets Monday, Wednesday and Friday 2:00-2:50pm, 443 Altgeld Hall
Office: 366 Altgeld Hall, tel: 265-5082
Office Hours: Monday 3:00-4:00pm and Thursday 4:00-5:00pm in 366 AH or by email appointment.
Text: J.R. Norris Markov Chains.

Homework	Due in class every Friday	30%
Test 1	Oct. 28-30, take-home, due in class on Friday	35%
Final Exam (post-midterm material)	Dec. 9-11, take-home, due in my office on Friday at 5pm	35%

The goal of this course is fairly rigorous understanding of Markov chains and Markov processes. We will go through Norris' book fairly linearly. Below is a rough and unordered list of some of the topics we will cover.

Introduction and Definitions of Markov property
Class Structure
Absorption Probabilities
Strong Markov Property
Measure Theory
Recurrence and transience
Recurrence and transience of Random Walks
Stationary distributions
Ergodic Theory
Jump Processes
Martingale Problem
Markov-Chain Monte Carlo