Lecturer

Wendelin Werner and Dominik Schröder

Coordinator

Daniel Contreras

Content

Measure theory formalism and probability theory, Dynkin's lemma and independence, convergence of series of independent random variables, law of large numbers, conditional expectation, martingale convergence theorems, uniform integrability, optional stopping theorem for martingales, the Galton-Watson process and its R-number, convergence in law and the central limit theorem, a bit of Markov chains and large deviations.

Lectures

Lectures will take place in-person at ML H 44 on Mondays from 10:15 to 12:00 and Wednesdays from 8:15 to 10:00.

Video Recordings

Lectures will be recorded and uploaded to the ETH Video Portal. You will receive the password soon by email.

Lecture Notes

• Lecture Notes (first part)
• Lecture Notes (second part, updated 20.12.22)
• Lecture Notes (third part, Apendix)

Exercises

The new exercises will be posted here on Mondays. You are welcome to submit your solutions, even though it is not mandatory. In case you decide to submit them, this needs to be done by the following Monday at 17:00 using the links in the table below. Your solutions will corrected and returned by email. Please follow the instructions below.

Instructions for Submission

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 student@ethz.ch_1.pdf.
3. Upload your solution using the links the table below, according to your surname (you will not see your file after submitting, since it is a polybox drop link).

Exercise classes

Students are distributed in 3 groups according to family name. Assitants will correct the exercises of their corresponding group. Nonetheless, you can enroll in any of the classes below in myStudies. Exercises classes start the second week of the semester.

Forum

In order to help you prepare the exam, we will open an online forum for the course on the 5th of december. You can access here (you may need to create a new forum account).

Office hours

Office hours are offered by group 3 on Mondays and Thursdays from 12:00 to 13:00 in HG G 32.6 starting the fourth week of the semester.

Additional literature

• D. Williams, Probability with martingales, Cambridge University Press 1991 (available online)
• R. Durrett, Probability: Theory and examples, Duxbury Press 1996 (online version)