University of Duisburg-Essen
Faculty of mathematics, Campus Essen
Martin Hutzenthaler (martin (dot) hutzenthaler 'at' due (dot) de)
Wolfgang Löhr (wolfgang (dot) loehr 'at' due (dot) de)

8.September 2014

Lecture with exercises (2SWS+1SWS) in the Winter term 2014/15
Lecture: Thursdays 12.15-14.00 (room WSC-S-U-3.03)
Exercises: Tuesdays 9.15-10.00 (room WSC-S-U-3.03)

Stochastic differential equations

Target audience:
This lecture is an in-depth module stochastics (Vertiefungsmodul Stochastik) for the master's programme (5ECTS). The work load is about 150 hours (45 hours of presence time).

The first lecture will be on Thursday, October 16, 2014. The exercises start on Tuesday, October 21, 2014.


  1. Martingale theory
  2. definition and properties of (local) martingales and semimartingales
  3. Ito Integrals
  4. Construction; Properties; Ito formula; martingale representation theorem;
  5. Ito formula
  6. Weak and vague convergence; Prohorov's theorem
  7. Stochastic differential equations
  8. examples of explicitly solvable SDEs; existence and uniqueness; strong and weak solutions; the Yamada-Watanabe pathwise uniqueness theorem; Martingale problems; Markov property
  9. Applications of SDEs

Students are required to be familiar with measure theory and conditional expectations, e.g., through the lecture 'Wahrscheinlichkeitstheorie 1' or through chapters 1-8 in Klenke's book

Wolfgang Löhr supervises the exercises. You will find all exercise sheets on this web page.

Moodle course:
There is a moodle course on 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 preferred - German.