**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.

[See also the evolving lecture notes, to be updated after each lecture.]

**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistical Sciences, University of Toronto.
Sidney Smith Hall (SS), room 5022; phone (416) 978-4594; e-mail
j.rosenthal@math.toronto.edu;
web http://probability.ca/jeff/

**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 10. Last class April 4. No class Feb 21 (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.

**Course Web Page:** Visit
probability.ca/sta447
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.

**Evaluation (TENTATIVE, MIGHT CHANGE!):**

28% Midterm #1 (two hours): Thurs Feb 7 during class time

28% Midterm #2 (two hours): Thurs Mar 21 during class time

44% Final Exam (three hours): some time during April 6-30,
to be announced later

**Notes:** On all tests and exams,
**BRING YOUR STUDENT CARD**,
and **DO NOT SIT NEXT TO ANYONE THAT YOU KNOW**,
and **NO AIDS ALLOWED** (not even calculators).
See also the various student services and academic resources available.
And, even if there are no graded homework assignments, you are still
strongly encouraged to attempt the **practice problems** in
the lecture notes and supplementary readings to learn the material well
and prepare well for the tests and exam.

**Instructor Office Hours:**
You are welcome to talk to the instructor after class, or any time you
find him in his office (SS 5022),
or you can e-mail him to arrange another time to meet.

**Supplementary Readings:**
There is no required textbook.
The instructor will post his rough
lecture notes
on this course web page after each lecture.
In addition, the following books (among others)
may be useful for further reading:

- R. Durrett (1999), Essentials of stochastic processes. Springer, New York. [See free online version of second edition, 2011.]
- G.R. Grimmett and D.R. Stirzaker (1992), Probability and random processes, second edition. Oxford University Press. [Or: third edition, 2001.]
- G.E. Lawler (1995, or 2nd ed. 2006), Introduction to stochastic processes. Chapman & Hall.
- O. Häggström (2002), Finite Markov chains and algorithmic applications. Cambridge University Press.
- S. Resnick (1992), Adventures in stochastic processes. Birkhauser, Boston.
- J.S. Rosenthal (2006), A first look at rigorous probability theory, 2nd ed. World Scientific Publishing Company, Singapore. [Especially chapters 7,8,14,15.]

**Lateness policy**:
Homework assignments (if any) are due **sharp** at the indicated time.
Lateness penalties are:
1-5 mins = 1 point;
6-10 mins = 2 points;
11-30 mins = 5% of total points;
31 mins - 24 hours = 10% of total points;
longer = (10% of total points) x (number of days late, rounded **UP**).

**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/homework paper to the instructor
**within one week** of when the graded work was first
available. **Warning: your mark may end up going down rather than up.**
(Note: for final exams, a different Faculty-wide process should be followed instead.)

This document is available at probability.ca/sta447 or probability.ca/sta2006, or permanently at probability.ca/jeff/teaching/1819/sta447/