Math 495 – Stochastic Processes

Renato Feres

Spring 2022

Section information

  • Class time and location: Tuesday and Thursday, 1:00PM to 2:20PM, Duncker 101
  • Office hours: Tuesday 2:30PM to 4:00PM and Friday 11:00AM to 1:00PM

Office hours will be in my office in Cupples I, room 17. I will also keep a Zoom meeting running during this time if you prefer/need to meet online.

Subject

This introduction to stochastic processes deals largely with discrete and continuous time Markov chains, continuous state processes (mainly Brownian motion) and stochastic simulation methods (Markov Chain Monte Carlo). We assume as prerequisites that the student has a good grasp of matrix algebra at the level of Math 309 and general probability at the level of Math 493.

As part of the coursework we will make use of R (the environment for statistical computing) to simulate examples of stochastic processes. I’ll have more to say about it later. I do not assume that you are already familiar with R.

Text

The textbook for the course is

  • Introduction to Stochastic Processes with R by Robert P. Dobrow, 2016, John Wiley & Sons.

I plan to follow it fairly closely.

Topics we will to cover.

The following topics correspond to chapters 1 through 8 of Dobrow’s textbook:

  1. Brief overview of probability theory
  2. Discrete-time Markov chains
  3. Branching processes
  4. Markov Chain Monte Carlo methods
  5. Poisson processes
  6. Continuous-time Markov chains
  7. Introduction to Brownian motion

If time permits, we’ll also cover briefly stochastic calculus (Itô calculus) based on the texbook’s chapter 9.

Coursework and grades

Coursework will consist of weekly homework assignments (I plan around 9 or 10 assignments), one mid-term exam and one final exam. Final grades are determined as follows: homework 60%, midterm 10%, final exam 30%. Your lowest homework grade will be dropped. Assignments will be handled through Crowdmark and grades will be posted on Canvas.

Grades may be curved, but will not be less than the following scale:

A+ A A- B+ B B- C+ C C- D F
TBA 90+ [85,90) [80,85) [75,80) [70,75) [65,70) [60,65) [55,60) [50,55) [0,50)

If you are taking this class Pass/Fail, you need a C- to pass. There is no requirement for auditing.

In writing the tests (mid-term and final), I will rely strongly on the homework assignments. To feel confident, you should master the topics and exercises covered by the assignments. Test questions will not involve R in any form.

Schedule of midterm exam and final

Test date time
MT March 10 1:00PM – 2:30PM
Final May 10 1:00PM – 3:00PM

Recording

I plan to record the in-person lectures using Zoom and make them available in Canvas. I expect, and strongly urge, that students will attend classes in person, but the option of attending online is available if you cannot be there for health related reasons.

Academic integrity

I will follow the University’s academic integrity policy, which you can read here. Work submitted under your name is expected to be your own. You are permitted, and encouraged, to collaborate on assignments. You may research broadly over the internet and in books when working on assignments.

If you have any concerns or questions about this policy or academic integrity in class, please contact me.

Email

Please include Math 495 in the subject line of any email message that pertains to this course.

Homework assignments

Weekly homework assignments will be posted below on this syllabus. Solutions will be posted in Canvas (under Pages).