Math 466/564/STAT 555: Applied Random Processes (Spring 2024)
This is an advanced undergraduate/graduate course on applied stochastic processes, designed for those students who are going to need to use stochastic processes in their research but do not have the measure-theoretic background to take the Math 561-562 sequence. Measure theory is not a prerequisite for this course. However, a basic knowledge of probability theory (Math 461 or its equivalent) is expected, as well as some knowledge of linear algebra and analysis. The goal of this course is a good understanding of basic stochastic processes, in particular discrete-time and continuous-time Markov chains, and their applications. The materials covered in this course include the following:
- Fundamentals: background on probability, linear algebra, and set theory.
- Discrete-time Markov chains: classes, hitting times, absorption probabilities, recurrence and transience, invariant distribution, limiting distribution, reversibility, ergodic theorem, mixing times;
- Continuous-time Markov chains: same topics as above, holding times, explosion, forward/backward Kolmogorov equations;
- Related topics: Discrete-time martingales, potential theory, Brownian motion;
- Applications: Queueing theory, population biology, MCMC.
Course | go.illinois.edu/math466 |
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Official Site | Canvas |
Student hours | TBA + by Appointment. |
Instructor | Partha Dey | ||||||||||||||||||
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Office | 35 CAB | ||||||||||||||||||
Contact | Email with subject "Math 466:" (Use your official @illinois.edu address). | ||||||||||||||||||
Class | TR 9:30am-10:50am in 163 Noyes Lab. | ||||||||||||||||||
Textbook | 1. Norris: Markov Chains, Cambridge University Press, 1998; | ||||||||||||||||||
Other Refs |
2. Levin, Peres, and Wilmer: Markov Chains and Mixing Times, AMS, 2009; 3. Grimmett and Stirzaker: Probability and Random Processes, 4th Ed., OUP, 2020. | ||||||||||||||||||
Prerequisite | Math 461 (Undergraduate Probability) and MATH 447/448 (Undergraduate Analysis). A basic knowledge of probability theory, linear algebra and analysis is expected. Measure theory is not a prerequisite for this course. | ||||||||||||||||||
DRES | To obtain disability-related academic adjustments and/or auxiliary aids, students should contact both the instructor and the Disability Resources and Educational Services (DRES) as soon as possible. You can contact DRES at 1207 S. Oak Street, Champaign, (217) 333-1970, or via e-mail at disability@illinois.edu. | ||||||||||||||||||
Grading Policy |
Homework: 40% of the course grade. Homework will be assigned weekly on Thursdays on Canvas, to be submitted before the start of next Thursday lecture in Canvas. Solving a lot of problems is an extremely important part of learning probability. You are encouraged to work together on the homework, but I ask that you write up your own solutions and turn them in separately. Late homework will not be graded. If for some reason you've done a homework but can't turn it in online, send it via email before class. Because of this strict policy on late homework, I will drop your lowest score. Please talk to the instructor in cases of emergency. Midterm : 25% will depend on an in-class midterm exam on Tuesday, Feb 27, 2024 in class. Final : 35% will depend on the final exam on Tuesday, May 7, 2024 at 7-10pm. Attendance & Participation: 3% of the course grade. | ||||||||||||||||||
Exam Policy | Make-up exams will be given only for medical or other serious reasons. If you discover that you cannot be at an exam, please let me know as soon as possible, so that we can make other arrangements. You must work completely on your own during exams. I make my exams fair and similar to homework, so as long as you use the resources provided, you should do fine. If you have difficulties of any kind or fall behind in the course, please come talk to me as soon as possible. | ||||||||||||||||||
Grading scale | Final scores will be converted to letter grades beginning with the following scale:
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