Autumn 2016

Instructor: Professor Steve Lalley

Office: 323 Jones Hall

Office Hours: Thursday 1:00 -- 2:00

Phone: 702-9890

E-mail:
`lalley "atsign" galton.uchicago.edu`

Course Assistant: Si Tang

Office Hours: Thursday 4 -- 5 p.m. Jones 308

Email: `sugar "atsign" uchicago.edu`

This course will introduce some of the major classes of stochastic processes: Poisson processes, Markov chains, random walks, renewal processes, martingales, and Brownian motion. A substantial part of the course will be devoted to the study of important examples, such as branching processes, queues, birth-and-death chains, and urn models. Students will be expected to have proficiency in elementary probability theory, undergraduate real analysis (especially sequences and series), and matrix algebra. Some familiarity with the theory of Lebesgue measure and integration would be helpful, but is not essential. There will be weekly problem assignments and midterm and final exams.

Required Text: None. Lecture Notes and Homework Assignments will be posted here.

Recommended Reading:

- Sheldon Ross, Stochastic Processes 2nd Ed.
- Greg Lawler, Introduction to Stochastic Processes, Second Edition
- W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1
- W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2

Midterm Exam: Friday, November 4

Final Exam: T. B. A.

Bookmark this page! I will post weekly homework assignments and lecture notes here.

- Poisson Processes
- Random Walk (sections 1,2,3.1-3.4 only)
- Renewal Processes
- Markov Chains
- Branching Processes
- Harmonic Functions
- Continuous-Time Markov Chains revised 11/15/2016
- Brownian Motion

Please Note: Assignment 5 is due on the Wednesday before the midterm exam. All other assignments will be due on Mondays.

- Assignment 1. Due: Monday October 3
- Assignment 2. Due: Monday October 10
- Assignment 3. Due: Monday October 17
- Assignment 4. Due: Monday October 24
- Assignment 5. Due: Wednesday November 2
- Assignment 6. Due: Wednesday November 16
- Assignment 7. Due: Wednesday November 23
- Assignment 8. Due: Wednesday November 30