MTH 202: Intro to Stochastic Processes

Overview

The official course description is succinct and clear: Theory and applications of random processes, including Markov chains, Poisson processes, birth-and-death processes, random walks.

MTH 202 is the sequel to MTH 201, Intro to Probability. In MTH 201, we studied the basics of probability theory like random variables and probability distributions. In this course, we will study random variables that have an additional time parameter; i.e., a stochastic process. We will primarily study a canonical discrete-time stochastic process called a Markov chain. Markov chains appear in many fields of science like physics, biology and economics. The theory will be supplemented by examples from these fields. Some examples of Markov chains and processes that we will study include Poisson processes, birth-and-death processes, random walks and queues. Time permitting, we will briefly touch upon the theory of martingales and Brownian motion. The course will not be mathematically rigorous, but we will give short proofs whenever they’re illuminating.

Instructor

Arjun Krishnan

• Lectures: MW 12.30 - 1.45pm Gavett 312
• Office: Hylan 817
• Office Hours: 11 - 12pm Mondays and Wednesdays in my office, or by appointment.
• E-mail: rochester at shirleyarjun dot net
• Teaching Assistant (TA): TBA
• TA Office Hours: TBA

Textbook

Mandatory:

Introduction to Stochastic Modeling, Karlin and Pinsky. You can get an older edition, and its essentially the same: Karlin and Taylor. You can also buy them second hand.

I do not recommend getting a pirated copy from libgen even if you cannot afford it. There are a few copies on reserve at Carlson Library.

This will be supplemented by material from the following books. Pdfs of whatever you need will be posted online.

• Introduction to Stochastic Processes, by Gregory F. Lawler.. We will use this for our Martingales Chapter.
• Introduction to Probability Models, Sheldon M. Ross.

Grading

Here is the grade distribution from the last time I taught it.

Guaranteed grades: if you make these scores, then you are guaranteed a letter grade in the following ranges.

I sometimes “curve up” linearly to help students with lower scores.

Homework

• Will be assigned every week on this webpage on Wednesday after class.
• You may choose to work with one other person. If you do, you must write both names on it, and receive the same grade.
• It will be due Wednesdays on gradescope.
• Lowest score will be dropped.
• You are encouraged to seek my help (or the TAs) either over email or during office hours.

Quizzes

In class quizzes, every Monday, based on previous weeks topics. It will consist of one or two problems.

Exams

Final: Tuesday, May 2 at 8.30AM in class.

Academic honesty

All assignments and activities associated with this course must be performed in accordance with the University of Rochester’s Academic Honesty Policy. More information is available at: www.rochester.edu/college/honesty. This resource is great, and has a great FAQ section. There are some fairly scary policies. For example, if you’re found cheating, the instructor is required to report you. I intend to follow this policy.

In this class, there are separate collaboration policies for HW, quizzes and exams. In short, you may collaborate on HW, but you must state it. You may not collaborate on quizzes.

Any usage whatsoever of online solution sets or paid online resources (chegg.com, chatGPT or similar) is considered an academic honesty violation and will be reported to the Board on Academic Honesty. In particular, any assignment found to contain content which originated from such sources is subject to a minimum penalty of zero on the assignment and a full letter grade reduction at the end of the semester (e.g. a B would be reduced to a C). This applies even if the unauthorized content was obtained through indirect means (through a friend for instance) and/or the student is seemingly unaware that the content originated from such sources. If you have any questions about whether resources are acceptable, please check with your instructor.

Help

If you are having difficulty seek help immediately - do not wait until it is too late to recover from falling behind. There are several avenues for you to get help and ask questions, outside of lecture:

• Attend instructor office hours or schedule an appointment to meet with your instructor.

• Undergraduate Study Hall: Mondays through Thursdays 5-8pm. It’s in Hylan 1104. There is no study hall from 3/13-3/14.

• There are also resources in the math department and at the university level.

Disability Support

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. You can reach the Office of Disability Resources at: (585)275-9049; 1-154 Dewey Hall. Or, visit Center for Excellence in Teaching and Learning.

To be granted alternate testing accommodations, you must fill out forms with CETL at least seven days before each and every exam. These forms are not sent automatically.