University of Duisburg-Essen
Faculty of mathematics, Campus Essen
(martin (dot) hutzenthaler 'at' due (dot) de)
Wolfgang Löhr (wolfgang (dot) loehr 'at' due (dot) de)
Lecture with exercises (2SWS+1SWS)
Winter term 2014/15
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
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.
- Martingale theory
definition and properties of (local) martingales and semimartingales
- Ito Integrals
Construction; Properties; Ito formula; martingale representation theorem;
- Ito formula
Weak and vague convergence; Prohorov's theorem
- Stochastic differential equations
examples of explicitly solvable SDEs; existence and uniqueness; strong and weak solutions;
the Yamada-Watanabe pathwise uniqueness theorem;
Martingale problems; Markov property
- 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
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.
- Rogers and Williams; Diffusions, Markov Processes and Martingales 2: Ito Calculus; Cambridge University Press; 2000
- Oksendal; Stochastic differential equations (6th edition); Springer; 2003
- Achim Klenke; Wahrscheinlichkeitstheorie; Springer; 2006
- Achim Klenke; Probability theory; Springer; 2008; translation of the book from 2006