University of Duisburg-Essen
Faculty of mathematics, Campus Essen
Prof. Martin Hutzenthaler

Lecture with exercises (4SWS+2SWS, 9ECTS) in the Summer term 2022
Lecture: Mondays 10:15-11:45 and Fridays 10:15-11:45
Exercises: Mondays 12.15-13:45

Stochastic differential equations

Target audience:
This lecture is an in-depth module stochastics (Vertiefungsmodul Stochastik) for the master's programme (9ECTS). The work load is about 270 hours (90 hours of presence time).

Please register in the moodle course Moodle page. The password is: sde2022

The first lecture will be on Monday, April 4, 2022.


  1. Reminder: Martingale theory
  2. definition and properties of (local) martingales and semimartingales
  3. Ito Integrals
  4. Construction; Properties; Ito formula; martingale representation theorem;
  5. Stochastic differential equations
  6. examples of explicitly solvable SDEs; existence and uniqueness; strong and weak solutions; the Yamada-Watanabe pathwise uniqueness theorem; Martingale problems; Markov property
  7. Numerical approximations of SDEs

Students are required to be familiar with martingales and with Brownian motion e.g., through the lecture 'Probability theory II' or through chapters 1-10,21 in Klenke's book

You will find all exercise sheets on the moodle course page to which everyone should register. News and messages will be sent over this moodle platform.

The language both in the lecture and in the exercises will be English or - if all agree - German.