Math 865 - Stochastic Processes I
Meeting MWF, 1-1:50PM, Snow 152
Office hours: Drop by, or email me for an appointment.
1.) Probability and Random Processes
2.) One Thousand Exercises in Probability
Both by Grimmett and Stirzaker
We will aim to cover the following chapters from the text, and also cover some other topics in more detail.
Quick review of Chapter 1+2+(Little bit of 7) to get used to the book's notation and style.
Selected topics from Chapters 5--13, depending on our interests.
There are many topics to choose from the textbook. We are open to suggestions.
Stein's method for Normal approximation (not in the textbook, we will follow Nathan Ross' survey)
Random walk (Chapters 3.9, 3.10, and also the book by Durrett Chapter 4.)
Branching Processes (Chapter 5.4)
Large Deviations (Chapter 5.11)
Markov Chains (Chapter 6) See also this textbook by Levin, Peres, and Wilmer.
Martingales (Chapter 7,12)
Random Processes and the Ergodic theorem (Chapter 8,9) See also these lecture notes by Sarig.
Brownian Motion (Chapter 13) See also the book by Morters and Peres.
Your grade will be based on a combination of homework, presentations, and tests. Students will have chances to present their own research, relevant topics of interest, and interesting exercises in class.
Rough grading schemes:
Presentations: Email me a few days in advance to let me know what you want to do, and how much time you expect it to take.
Homework: Do some of the exercises assigned in class and in the lecture notes.
I'll try to type out all the exercise assigned in class, and I might also come up with a few more
Hand them in when you are ready, but please don't wait till the end of the semester!
Feel free to discuss the exercises with your classmates or ask me for help.
Test 1: Feb 27. test1.pdf
Test 2: April 27 test2.pdf
Homework deadlines: April 15 for exercises that have appeared before Spring break and May 6 for exercises that have appeared after the break.
Presentations: Please come and see me before the Easter holiday.
Test 1 10%
Test 2 10%
Test 1 10%
Test 2 10%
Test 1 25%
Test 2 25%
(Your mark will the maximum of the marks of each scheme.)
Some lecture notes and exercises.
Some recommended exercises from the text for self-study and review. You may have already seen similar questions in previous courses. The solutions appear in One Thousand Exercises in Probability.
1.22, 1.24, 1.35, 1.5.1, 1.8.14, 1.8.16, 1.8.17, 1.8.18
3.4.7, 3.52, 3.11.13, 3.11.18, 3.1135, 3.11.40
5.6.1, 5.6.2, 5.6.3, 5.6.4, 5.6.5
6.1.2, 6.1.7, 6.1.8, 6.3.9, 6.5.6, 6.14.4, 6.15.43, 6.15.44,
7.11.16, 7.11.17, 7.11.21
Finite Markov chains and algorithmic applications, Haggstrom
Lectures on the coupling method, Lindvall
Markov Chains, Norris
Probability theory and example, Durrett
Probability with martingales, Williams
Ergodic theory, Petersen
Some more presentation topics. We are open to suggestions from the textbook or other papers/sources. You may need to be at school for these links to work: