STA 4502S: Topics in Stochastic Processes (Winter 2020)

This course will focus on convergence rates and other mathematical properties of Markov chains on both discrete and general state spaces. Specific methods to be covered will include coupling, minorization conditions, spectral analysis, and more. Applications will be made to card shuffling and to MCMC algorithms.

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Sidney Smith Hall, room 5022; phone (416) 978-4594; e-mail; web

Lecture Schedule: Wednesdays 11:10 - 1:00 in SS 2101. First class Feb 26. Last class April 1.

Note: This is a six-week class, and only counts for 0.25 course credit. The add date is any time before the second lecture. The drop date is end of the day of the second lecture.

Course Web Page: Visit for course information and announcements.

Prerequisites: Graduate-level probability theory with measure theory at the level of STA2111, and stochastic processes at the level of STA447/2006 (may be concurrent), plus basic familiarity with MCMC algorithms. This course is intended primarily for graduate students in statistics; all others must obtain permission from the instructor before enroling.

Readings: There is no required textbook. We will approximately follow these notes (pdf, transcribed by previous students). In addition, some of the material is covered in this paper / older version (discrete case), and this paper and this paper and Section 2 of this paper (general case). For basic background on Markov chains, see e.g. this book.

40% class participation (all six classes; see below)
50% homework (due at beginning of final class; see below)
10% presentation (in final class; see below)

For class participation, students are expected to punctually attend class each week, to pay close attention during class [no cell phones or laptops except for direct class-related purposes with prior permission], answer questions posed by the instructor, ask their own questions, discuss the material actively, review the previous material and notes before each new lecture, and show interest and enthusiasm in the course material.

For the homework, students should solve in detail, with full explanation, all 14 of the Exercises at the end of the first paper older version, and write them up clearly and neatly.

The presentations will take place in the final class, and will be a maximum of 15 minutes each, and should present the ideas behind your solutions to a few interesting homework problems. (Note: claim your problems early, to avoid duplication with other presentations.)

Instructor Office Hours: You are welcome to talk to the instructor after class, or any time you find him in his office, or you can e-mail him to arrange another time to meet.

Challenges? If you encounter challenges during your studies, then please visit Academic Success or the Health and Wellness Centre for assistance and support.

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