Course descriptionBrownian motion is a fundamentally important stochastic process, discovered in the contexts of financial markets and statistical physics. It relates to diverse mathematical topics from partial differential equations to constructive quantum field theory. This course introduces you to the key techniques for working with Brownian motion, including stochastic integration, martingales, and Ito's formula.
- Brownian motion
- Stochastic integral
- Itō's formula and applications
Time2017-2018 Period IV (6 weeks)
- Lectures: Mondays 10-12 in M3 and Wednesdays 10-12 in M3 (2 x 2h lectures / week)
- Exercise sessions: Wednesdays 14-16 in Y307 (1 x 2h exercises / week)
PrerequisitesProbability theory (MS-E1600), Stochastic processes (MS-C2111) or equivalent.
GradingThe course grade is determined by a score consisting of:
- up to 24 points from the exam (4 problems worth 6 points each)
- up to 6 bonus points from exercises.
It is possible to get the maximum grade based on the exam alone, but of course the recommended method of studying is to continuously solve exercise problems during the course.
ExamThe exam will be held on:
- Wednesday 04.04.2017 at 13:00-16:00
There will be just one more time in 2018 to take the exam:
- Friday 25.05.18 at 13:00-16:00
You are allowed to bring to the exam a handwritten memory aid sheet. The memory aid sheet must be of size A4 with text only on one side, and it must contain your name and student number in the upper right corner. You don’t need to return your memory aid sheet. The exam consists of 4 problems, each worth 6 points.
- Results of exam on 04.04.2018
ExercisesThere are weekly problem sets, posted under the "Assignments" tab on this page. Written solutions to the problems are to be returned to the course homework folder (on the announcement board next to office Y249d) by Mondays at 10 am.
In the exercise sessions on Wednesdays 14-16, the course teaching assistant Alex Karrila will provide help in solving the problems. The exercise sessions also contain brief recitations on the topics of the lectures and problems. You should think about the problems in advance, so as to be able to focus on whatever you find difficult when the teaching assistant is there to instruct you!
- Durrett, R. Stochastic calculus: a practical introduction. CRC Press, Probability and Stochastics Series, 1996.
Freely available online notes corresponding roughly to the course contents:
- Berestycki, N. Stochastic calculus.