This course gives an introduction to Brownian motion and stochastic calculus. The following topics are planned:
Familiarity with measure-theoretic probability as in the standard D-MATH course Probability Theory will be assumed. Textbook accounts can be found for example in
Lectures take place live only on Tuesdays 8:15-10:00 and Thursdays 8:15-10:00 in HG E3.
The lecture on February 27 will take place in ML D28.
There will be no recordings.
The lecture notes are available here. The password will be emailed to the enrolled students.
The lecture notes will be updated and extended throughout the semester.
Please be advised that the lecture notes are protected by copyright, and their dissemination in any form is strictly prohibited.
Exercise classes take place live only on Fridays 8:15-9:00 in HG G26.5 (for last names A-I), 9:15-10:00 in HG G26.5 (for last names J-R) and 12:15-13:00 in HG G26.3 (for last names S-Z).
The first exercise class is on February 21, in the first week of the semester.
New exercise sheets are uploaded below on Wednesdays before the corresponding Friday exercise class, along with solutions to the exercise sheet from the previous week.
While handing in your solutions is not compulsory, experience shows that being able to solve the exercises independently goes a long way towards good exam performance. We strongly encourage you to hand in written solutions. This can be done electronically. Please follow the instructions below.
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.
| Exercise Sheet | Due by | Solutions |
|---|---|---|
| Exercise Sheet 1 | February 26, 2025 | Solution 1 |
| Exercise Sheet 2 | March 5, 2025 | Solution 2 |
| Exercise Sheet 3 | March 12, 2025 | |
| Exercise Sheet 4 | March 19, 2025 |
The exam will be in person, oral and closed book. Each candidate will receive a question and have 20 minutes to prepare for the exam. The preparation is also closed book, and the question studied by the candidate will be the starting question in the exam, which lasts for 20 minutes.
Students should bring for the exam an identification document and some paper to write on during their preparation time. No other aids are allowed, and mobile phones must be put away during the preparation time. Also, to anticipate a potential question — there is no available list of the possible questions. The material for the exam comprises all the material covered in the lecture notes and all the material covered in the exercise sheets. Students are expected to have a good overview of the material, understanding both the ideas and the proofs of the results.
Some material may be taken out from the material covered by the exam. This will be communicated later, towards the end of the semester.