University of Duisburg-Essen
Faculty of mathematics, Campus Essen
Prof. Martin Hutzenthaler
February 2, 2016
Lecture with exercises (2SWS+1SWS, 6ECTS)
Summer term 2016
Mondays 13.30-15.00 (room WSC-N-U-3.04)
Exercises: Mondays 12.15-13.00 (room WSC-N-U-3.04)
Stochastic differential equations and their approximations
This lecture is an in-depth module stochastics (Vertiefungsmodul Stochastik)
for the master's programme (6ECTS).
The work load is about 180 hours (45 hours of presence time).
The first lecture will be on Monday, April 11, 2016.
The exercises start on Monday, April 18, 2016.
- Reminder: Martingale theory
definition and properties of (local) martingales and semimartingales
- Ito Integrals
Construction; Properties; Ito formula; martingale representation 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
- 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.
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