Introduction to Theory and Numerics of Stochastic Differential Equations

Professor: JProf. Dr. Diyora Salimova
E-Mail Professor: diyora.salimova@mathematik.uni-freiburg.de
Lecture: Wednesdays 12-14, SR 226, Hermann-Herder-Str. 10
Office Hours: by arrangement, R 208, Hermann-Herder-Str. 10
Tutorials: Thursdays 14-16, SR 226, Hermann-Herder-Str. 10
Assistant: M.Sc. Ilkhom Mukhammadiev
E-Mail Assistant: ilkhom.mukhammadiev@mathematik.uni-freiburg.de
Office Hours: by arrangement, R 210, Hermann-Herder-Str. 10

Updates

  • Note that the last sheet, Exercise sheet 9, has 2 weeks deadline. Hence there will be no exercise class on 16.06.2026. Instead we will offer an online office hour (Zoom link will be sent via email).
  • Oral exams will take place from the second half of August. Incase you wish to take one contact the lecturer to fix the exact date.

Content

The aim of this course is to enable the students to carry out simulations and their mathematical analysis for stochastic models originating from applications such as mathematical finance and physics. For this, the course teaches a decent knowledge on stochastic differential equations (SDEs) and their solutions. Furthermore, different numerical methods for SDEs, their underlying ideas, convergence properties, and implementation issues are studied. The topics we will cover
  • Preliminaries from measure and probability theory
  • Generation of random numbers
  • Monte Carlo integration methods
  • Stochastic processes and Ito calculus
  • Stochastic difeerential equations (SDEs)
  • Numerical approximations for SDEs
  • Applications to computational finance: Option valuation

Studien-/Prüfungsleistungen

Studienleistung: Achieving 50 % of exercise points.

Prüfungsleistung: Completion of the Studienleistung and successful participation in the oral exam.

Lecture Notes

The lecture notes will be regularly uploaded here: Version 19.06.2026

Exercise Groups

Tutorials begin during the second week of lectures and take place weekly.

Exercise Sheets

Exercise sheets will be a mixture of theoretical as well as Matlab exercises. We will also give a short Matlab tutorial for beginners. Details on the usage of MATLAB as well as its installation on your computer you find here.

Submission at the letterbox NumSDE next to CIP-Pool (Hermann-Herder-Str. 10) or via e-mail until Tuesday. Please send your Matlab solutions as a zip-Data (except of the case it is just one file) per E-Mail to Ilkhom. The exercise sheets can be submitted in groups of two. In that case an equal contribution from both of the students is expected.
 Sheet Uploaded Submission deadline
Sheet 1 27.04.2026 Thursday, 07.05.2026, at 16:00
Sheet 2 07.05.2026 Tuesday, 19.05.2026, at 16:00
Sheet 3 19.05.2026 Tuesday, 02.06.2026, at 16:00
Sheet 4 02.06.2026 Tuesday, 09.06.2026, at 16:00
Sheet 5 09.06.2026 Tuesday, 16.06.2026, at 16:00
Sheet 6 16.06.2026 Tuesday, 23.06.2026, at 16:00
Sheet 7 23.06.2026 Tuesday, 30.06.2026, at 16:00
Sheet 8 29.06.2026 Tuesday, 07.07.2026, at 16:00
Sheet 9, Templates 06.07.2026 Tuesday, 21.07.2026, at 16:00

Literature

  1. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations Springer-Verlag, Berlin, 1992.
  2. Bernt Oksendal: Stochastic Differential Equations Springer, 2003.