Introduction to stochastic processes

Instructor: Yaniv Plan
Office: 1219 Math Annex
Email:  yaniv (at) math (dot) ubc (dot) ca

Lectures: MWF 9:00 am – 10:00 am,  SWNG 121

Office hours: M 11:30 am – 12:30 pm, F 2:00 pm – 3:00 pm, MATX 1219

Outline: Here.

Piazza:  Sign up link here.

Textbook:  S. M. Ross, “Introduction to Probability Models”, 11th edition, Academic Press. Earlier editions are indistinguishable for our purposes apart from possible changes to page and problem numbers. An optional more advanced reference: G.R. Grimmett and D.R. Stirzaker,“Probability and Random Processes”, 3rd edition, Oxford, (2001).

There are interesting resources at:

Discussion board: We will use a Piazza discussion board this term. You can ask questions regarding the course there, and answer other students’ questions. Do not share solutions to assignments on Piazza before the due date.

Grading:  The final mark will be based on homework (10%), two midterm exams (20% each),
and final exam (50%). Term marks may be scaled for consistency in both sections of MATH 303.

Tests: There will be two 50-minute midterms during class.  Midterm I on Wednesday, February 14, and Midterm II on Wednesday, March 21.

Final Examination: will take place in the April examination period. Please do not make travel
plans before the exam schedule is announced.

Missed mid-terms and assignments will normally receive a zero grade. Exceptions may be
granted by prior consent from the instructor, or for a documented medical emergency. In
the latter case, the instructor must be notified within two working days of the missed test, and
presented with a doctor’s note immediately upon the student’s return to UBC. When an exception
is granted for a missed test, there is no make-up test, and the final exam mark will be used.

Lectures* (written on computer, handwriting may suffer).

Lecture 1: Basic definitions.  Warm-up 2-state Markov chain limiting behaviour.
Lecture 2: Chapman Kolmogorov equations.  Probability distribution after n-steps of a Markov Chain.
Lecture 3: Gambler’s ruin. (For some extra material on linear recurrence relations, see some brief notes here and the videos here.)
Lecture 4:  Classification of states.  Partition into communicating classes.  Periodicity, recurrence.
Lecture 5:  Properties of transience/recurrence.
Lecture 6:  Recurrence/transience of random walk on Z^d.
Lecture 7:  Limiting probabilities.

*Based on a set of lecture notes by Gordon Slade.

Reading ahead:  Here is a rough outline of material covered week by week, including book sections and other helpful learning materials.  This was compiled by Richard Balka, and is from a previous iteration of this class.  It will approximately, but not exactly, match our syllabus.

Homework: 9 weekly assignments will be given. These are due at the beginning of class on
the due date, almost each Wednesday. No later assignments will be accepted. The single lowest
assignment will be ignored.

Due January 17: Homework 1.
Due January 24: Homework 2.
Due January 31:
Due February 7:
Due February 28:
Due March 7:
Due March 14:
Due March 28:
Due April 4: