Lecturer

Vincent Tassion

Coordinator

Ritvik Radhakrishnan

Course Catalogue

401-3601-00L

Content

1. Fundamental results: law of large numbers, different notions of convergences for random variables, characteristic functions, convergence in law, central limit theorem.
2. Martingales: conditional expectation, almost sure convergence, optional stopping theorem.
3. Markov chains: definition and Markov property, classification of states, convergence to equilibrium.

Lectures

There are two lectures per week: Wednesday, 12:15 to 14:00 at ML H44 and Friday, 10:15 to 12:00 at CAB G11 .

Lecture notes

• Introduction and reminders
• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9

Lecture recordings

You can find the recordings here . The username and password were sent by email.

Exercises

We strongly encourage you to hand in written solutions. This can be done electronically following the instructions below.

1. Make sure you're registered for one of the problem classes in myStudies.
2. Scan your solution into a single PDF file.
3. Name the created file as {email address}_{exercise sheet number}.pdf (e.g. andrey.kolmogorov@probability.com_1.pdf).
4. Upload your solution using the link in the table below (please submit to the problem class you registered for) before 18:00 on the indicated Friday.

Late submissions will not be considered. In case you submit your solution early and then decide to change something and submit again, we will only consider the most recent submission.

Note that only exercises marked with [R] (which stands for recommended) will be corrected.

Exercise sheets

Exercise classes

Exercises classes start from the second week of the semester.

Note: If you spot any typos or mistakes, please email ritvik.radhakrishnan@math.ethz.ch.