Applied Stochastic Processes Spring 2021

Vincent Tassion
Laurin Köhler-Schindler


Stochastic processes are a way to describe and study the behaviour of systems that evolve in some random way. In this course, the evolution will mostly be with respect to a scalar parameter interpreted as time, so that we discuss the temporal evolution of the system. We introduce several important classes of stochastic processes, analyse their properties and behaviour and show by some examples how they can be used. The main emphasis is on theory; in that sense, "applied" should be understood to mean "applicable".

Outline of the course:


Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L).

Lecture Notes

Lecture notes will be regularly updated.

In addition, you can access the notes of lecture 12, the notes of lecture 13, and the notes of lecture 14. As mentioned in class, the lecture notes on continuous-time Markov Chains will possibly be made available at a later stage (for continuous-time Markov chains (Chapter 6), only the material from the notes of lectures 13-14 and the exercises are relevant for the exam).

You can also find the lecture notes by Prof. Sznitman (spring semester 2017) here.


Lectures take place online via Zoom each Tuesday from 09:15 to 12:00. Exercise classes also take place online via Zoom on Thursdays as indicated below. The Zoom links have been communicated by email to registered students. If you are a registered student and you need the link to be sent again, you can contact the coordinator of the course.

If you have any questions related to the content of the lectures or the exercises, you are very welcome to ask them on the forum.

Even though we recommend to attend the lectures live, recordings will be made available on the ETH video portal. The login details have been sent to all registered students by email. Please note that exercise classes will not be recorded to keep an interactive atmosphere and encourage spontaneous questions and discussions.


The new exercises will be posted here every week on Wednesday. We recommend to look at the problems and prepare some questions before the exercise classes on Thursday.

Exercise sheet Due by Solutions
Exercise sheet 1 March 1 Solution 1
Exercise sheet 2 March 8 Solution 2
Exercise sheet 3 March 15 Solution 3
Exercise sheet 4 March 22 Solution 4
Exercise sheet 5 March 29 Solution 5
Exercise sheet 6 April 12 Solution 6
Exercise sheet 7 April 19 Solution 7
Exercise sheet 8 April 26 Solution 8
Exercise sheet 9 May 3 Solution 9
Exercise sheet 10 May 10 Solution 10
Exercise sheet 11 May 17 Solution 11
Exercise sheet 12 May 24 Solution 12
Exercise sheet 13 May 31 Solution 13
Exercise sheet 14 June 7 Solution 14


You are welcome to submit your solutions, even though it is not oligatory. In case you decide to submit your solutions, this needs to be done before 18:00 of the corresponding due date (typically on Monday). Your solutions will then be corrected and returned by e-mail. Please follow the instructions below.

  1. Scan your solution into a single PDF file. File format other than PDF will not be accepted. In case you do not have access to a scanner, scanning to a single PDF can be done efficiently using mobile applications such as Google Drive or Adobe Scan and many other ones. Please make sure that your scans are of good quality if you use these apps.
  2. Name the created file as {email address}_{exercise sheet number}.pdf. The parts surrounded by brackets are placeholders that should be replaced by the email address at which you want to receive the corrected solution and the number of exercise sheet for which you are submitting a solution, respectively. A correctly named solution file for exercise sheet 1 is for instance given by markov.chain@probability.com_1.pdf.
  3. Upload your solution using either the link A-L or the link M-Z in the table below (according to your surname).
Several comments are in order:

Exercise classes

First exercise class: Thursday, February 25

Enrollment and hand-in: The enrollment to the exercise classes by surname (see below) is binding for the submission of your solutions, but not for your attendance. This means that you can attend the exercise class that fits best with your schedule, but you need to submit your solutions according to your surname.

Time and location:

Thursday, 09:15-10:00Online Laurin Köhler-Schindler A-L
Thursday, 12:15-13:00Online Daria Sakhanda M-Z