Probability Theory Autumn 2020

Prof. Dr. Alain-Sol Sznitman
Daniel Contreras Salinas
Time and location
Tuesday 10:15 - 12:00 and Thursday 10:15 - 12:00 via live streaming. Videos of each lecture will be available shortly after here

Course Content

This course presents the basics of probability and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.

Lecture Notes

An electronic version of the lecture notes is available for registered students.

Exercise classes

Exercise classes will take place every week starting from the 22 of September.

Online class

All students will be by default enrolled in the online exercise class. The exercise classes until the end of the semester will take place via Zoom. You will receive the information to access by email. Each Tuesday a recording of one of the exercise classes will be available here.


The exercise sheets will be published on Monday in the table below. The exercises will be then discussed during the exercise class, and turned in a week later.

Please hand in your solutions by the following Tuesday at 12:00, following the instructions below.

Instructions for submission:

To submit your solutions please follow the steps below:
  1. Write down your name in the first page of your solutions.
  2. If you have written your solutions on paper, please scan all the pages in order and create a pdf file. If you do not have a scanner we recommend that you use applications like CamScanner or OfficeLens. If you wrote your solutions on a tablet, export the file to pdf format.
  3. Rename your file using your email account followed by the number of the exercise sheet. For example, if your email address is "" and you want to submit the third exercise sheet, you need to rename your file "username@student.ethz.ch_3.pdf". You can use any mail you prefer here.
  4. Click on the link corresponding to the exercise sheet and your last name initial letter, enter the password of the lecture and drop your file. You will receive your solutions back to the email you chose before the next exercise class.
  5. Files that are not in the format above might not be turned back.
Exercise sheet Due by Submission Solutions
Exercise sheet 1 September 29 A-L M-Z Solutions 1
Exercise sheet 2 October 6 A-L M-Z Solutions 2
Exercise sheet 3 October 13 A-L M-Z Solutions 3
Exercise sheet 4 October 20 A-L M-Z Solutions 4
Exercise sheet 5 October 27 A-L M-Z Solutions 5
Exercise sheet 6 November 3 A-L M-Z Solutions 6
Exercise sheet 7 November 10 A-L M-Z Solutions 7
Exercise sheet 8 November 17 A-L M-Z Solutions 8
Exercise sheet 9 November 24 A-L M-Z Solutions 9
Exercise sheet 10 December 1 A-L M-Z Solutions 10
Exercise sheet 11 December 8 A-L M-Z Solutions 11
Exercise sheet 12 December 15 A-L M-Z Solutions 12
Exercise sheet 13 December 22 A-L M-Z Solutions 13

Self evaluation Quiz

You can find your corrected solutions here. The password for your file is the second part of the filename you chose. You can also find the solution of the Quiz here.

Office Hours

Tu 15:30-16:30Calypso Herrera
We 11:00-12:00Daniel Contreras


The online versions are available online via NEBIS. These books are available as "Präsenzexemplare" in the mathematics library (HG G 7).