Math 4740: Stochastic Processes

Spring 2014

MWF 9:05-9:55 in 251 Malott Hall

Personnel

Professor: Lionel Levine
- Office hour: Mon 10-11, Thurs 3-4 in Malott 438

Teaching Assistant: Vardan Verdiyan

Office hour: Thurs 5-7 in Rhodes 657

Grader: Tom Chen

Study group session: Weds 3:30-4:30 in Malott 203

Course home page (this page): http://www.math.cornell.edu/~levine/4740

This page is under construction as we speak.

Piazza page for course discussions. Please go there now to take the poll about office hours.

Topics

Markov chains: strong Markov property, transience and recurrence, irreducibility, periodicity, stationary distributions and convergence.
Poisson process: exponential waiting times, memorylessness, thinning and superposition.
Martingales: gambling and prediction interpretations. Stopping times, optional stopping theorems and applications. Harmonic functions.
Continuous time Markov chains, and introduction to Brownian motion.

Extra topics as time permits and according to student interest: random walks and electrical networks, percolation, Ising model, random graphs, pagerank, Kelly criterion, prediction markets, mixing times, Markov Chain Monte Carlo (MCMC) and Metropolis-Hastings algorithm.

Prerequisite: An introductory probability course such as MATH 4710, BTRY 4080, ORIE 3600, ECON 3190. General proficiency in calculus and linear algebra. You will get more out of this class if you like and appreciate proofs. If unsure about your preparation, please discuss it with me.

Textbook

Introduction to Stochastic Processes, by Lawler.

Other sources

Lawler's book gets right to the point. If you like to see more examples worked out in detail, take a look at these books which cover roughly the same material:

Introduction to Probability Models, by Ross
Introduction to Stochastic Modeling, by Taylor and Karlin

For the extra topics, we may dip into a couple more advanced books:

Markov Chains and Mixing Times, by Levin, Peres and Wilmer
Probability on Trees and Networks, by Lyons (with Peres)

Problem Sets

Approximately weekly. Usually you will get the problem set on Friday and it is due at the beginning of class the following Friday. The first problem set will be posted by this Friday and due on Friday Jan 31.

Please check out the problem set guidelines for how to write a good solution.

You are encouraged to type your problem sets using LaTeX (or LyX). LaTeX is very versatile and widely used for writing technical documents of all kinds. It will serve you well if you go on in math or another technical field. Besides, you will need it for your project! Neatly handwritten problem sets are also acceptable.

Here is a video tutorial to get you started with LaTeX. Another good resource is the LaTeX wikibook. The Cornell math support center can help you get LaTeX up and running. (Ask for a math major tutor!)

Two times during the semester, you may have an automatic 72-hour extension on a problem set. Just hand it in at the beginning of the next class with a note saying you are using an extension. Otherwise, late homework will not be accepted except in an emergency (in which case you must inform me as soon as possible). Note: the problem set is due at the beginning of class. Handing it in after class starts will use up one of your extensions.

Group work policy: Working together with other students to solve the problems is strongly encouraged! You must list the group members at the top of your problem set and write the solutions entirely in your own words. Examples:

Figuring out the solution together on a blackboard and consulting the blackboard while you write up your solution: kosher
Giving your written solution to another student to copy with trivial wording changes: not kosher

Exams

Two in-class prelims on Friday, March 7 and Friday, May 2. The exams are closed book.

If a conflict prevents you from completing the exams on these dates, please let me know immediately.

Course Project

The course project allows you to explore a topic of your choice in depth. You will choose a peer-reviewed journal article that uses stochastic processes to model some real world phenomenon, and write a critical summary of the article analyzing the strengths and weaknesses of the model it proposes.

Check out the project guidelines for details.

First draft due by the beginning of class on Friday, April 18.
Final version due by the beginning of class on Friday, May 7.

Grading

Problem Sets: 40%. All problem sets count equally, none are dropped.
Two Prelims: 20% each
Course Project: 20%

Graduate students: If you are taking the course for credit, you will need to complete all the regular coursework (homework, exams and project), and will be assigned a grade like any other student. If you are taking the course S/U, you still need to do the coursework; I will compute a letter grade as usual and then assign you an S if the letter grade is at least C-. If you are not interested in doing the coursework, you are welcome to audit the course instead.

Laptop-free zone

Recent experiments show that even though people feel like they are accomplishing more when they multitask, they actually accomplish less. Higher level mathematics really demands your full attention. It's hard enough to learn stochastic processes without the temptation of facebook and xkcd (yes, the lure of xkcd is strong. very strong.) So please keep laptops, ipads, phones and other gizmos in your bag during class. If you must use a device during class (for example, to take notes on your tablet or laptop), you may do so in the back row where it does not distract anyone.

Students with disabilities

The Cornell disability policy is as follows. If you have a disability‐related need for reasonable academic adjustments in this course, provide me with an accommodation letter from Student Disability Services. Students are expected to give two weeks notice of the need for accommodations. If you need immediate accommodations, please arrange to meet with me within the first two class meetings.

Academic integrity

Please read carefully the group work policy for problem sets. I, your classmates, and the entire Cornell community expect you to complete this course based on your own work, to abide by relevant rules for coursework and exams, and to clearly attribute any use of the work of others. The Cornell Academic Integrity Policy spells out the nasty details of what happens otherwise.