NOTE: The teaching and assessment methods and timetable are subject to changes due to the emergency measures in place during the ongoing pandemic.
We will in particular use this Slack-workspace as the primary means of communication during the course, although all assignments and material will also be found through this MyCourses page.
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
TeachersKalle Kytölä (lecturer)
- Lectures: Tuesdays 10-12 in M3 and Wednesdays 14-16
in M2(online via Zoom, see Lectures-tab or Slack)
- Exercise sessions:
Thursdays 14-16 in M3Fridays 14-16 (via Slack)
PrerequisitesProbability theory (MS-E1600), Stochastic processes (MS-C2111) or equivalent.
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.
ExercisesThere are weekly problem sets, posted under the "Assignments" tab on this page.
- Le Gall, J.-F. Brownian Motion, Martingales, and Stochastic Calculus. Graduate Texts in Mathematics, volume 274, 2016.
- Durrett, R. Stochastic calculus: a practical introduction. CRC Press, Probability and Stochastics Series, 1996.
- Berestycki, N. Stochastic calculus.