STA 447/2006S: Stochastic Processes (Winter 2020)

STA 447/2006S is a course about random (stochastic) processes, designed for senior undergraduate and graduate students in statistics and related disciplines.

Tentative list of topics to be covered: Markov chains in discrete and continuous time, martingales, Poisson processes, renewal theory, and Brownian motion, with applications (as time permits) to Monte Carlo algorithms, random walks on graphs, branching processes, option pricing, queueing theory, and more.

Textbook: A First Look at Stochastic Processes, by J.S. Rosenthal (World Scientific). [Bookstore, Publisher, Amazon, Indigo, Kindle, Kobo, errata]

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

Lectures: Thursdays, 6:10 - 9:00 p.m., in room 128 of the Mining Building (170 College St.; building "MB" on campus map). First class Jan 9. Last class April 2. No class Feb 20 (Reading Week). During lectures, please put away your laptops and cell phones (unless you are using them specifically for a class-related purpose with prior permission), and pay attention to the material being presented. Note: The lectures will follow the textbook quite closely, so it is not necessary to take notes, you should just pay close attention to learn the material well and then use the textbook for later reference. UPDATE: The final two lectures will now be held ONLINE; see announcement, description.

Course Web Page: Visit for course information and announcements.

Prerequisite: STA347. NOTE: This prerequisite will be strictly enforced for undergraduate students: undergraduate students without STA347 will not be permitted to remain in STA447 except in very special circumstances. (It does not suffice to simply have taken some other advanced statistics courses.) For graduate students, it suffices to have taken a course equivalent to STA347 at another university; if you are unsure about the equivalence then please ask me. (For basic probability background, see e.g. Chapters 1-4 of this free book. And, for brief but important background for the course, read the textbook's Appendix carefully.)

50% Midterm #1 (135 minutes): Thurs Feb 6 during class time. See solutions.
50% Midterm #2 [TO BE HELD ONLINE]: Thurs Mar 19 during class time. See announcement, info, instructions, solutions.
0% Final Exam [CANCELLED DUE TO COVID-19]. See announcement.

Homework: There are no graded homework assignments. However, you are strongly encouraged to attempt the textbook's practice problems to learn the material well.

Notes: On all in-person tests and exams, BRING YOUR STUDENT CARD, and DO NOT SIT NEXT TO ANYONE THAT YOU KNOW, and NO AIDS ALLOWED (not even calculators). The tests will cover all lecture material up to that time. It is important to EXPLAIN your solutions clearly. If you continue an answer on the back of the page, write "OVER". It is important that you follow the university's Code of Behaviour at all times. If you are ill, then you should NOT take the test, but instead have a medical professional fill in this form.

Upcoming Instructor Office Hours, TO BE HELD ONLINE on "Bb Collaborate" on Quercus: Wed Mar 18 at 2:10-4:00. You can also e-mail him to ask questions.

Upcoming TA Office Hours, TO BE HELD ONLINE on "Bb Collaborate" on Quercus: Monday March 16 from 2:00 to 4:00. Tuesday March 17 from 10:00-12:00. Tuesday March 17 from 12:00 to 2:00. Wednesday March 18 from 10:00-12:00. Thursday March 19 from 10:00-12:00. Thursday March 19 from 12:00-2:00. You can also email the TAs at and to ask questions.

Supplementary Readings: In addition, the following books (among others) may be useful for further reading:

Regrading policy: Regrading requests should only be made for genuine grading errors, and should be initiated by writing or typing a complete explanation of your concern (together with your full name, student number, e-mail address, and telephone number) on a separate piece of paper, and giving this together with your original unaltered test/exam/paper to the instructor, within one week of when the graded work was first available (not counting Reading Week). WARNING: If the instructor does not find any genuine grading errors, then your entire paper might get re-graded firmly, with a critical eye, and your mark might well go DOWN rather than up. More details are here. (Note: for the final exam, a different Faculty-wide process should be followed instead.)

Midterm #2 regrading policy: Please first read the regrade policy, and think very carefully, before requesting a regrade. Regrading requests should only be made for genuine grading errors, otherwise your entire midterm might get re-graded firmly, and your mark might well end up going DOWN rather than up. Since Midterm #2 was online, regrading requests should instead be emailed directly to, with subject line "STA447/2006 Midterm #2 regrading request". As before, your request should be sent within one week of when the graded work was first available, and should include a complete explanation of your concern, together with your full name, student number, e-mail address, and telephone number. (Note: You might not receive a direct reply to your email. Any resulting grade adjustments might not be entered on Quercus, but will be used to calculate final course grades.)

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

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