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

February 2, 2016

Lecture with exercises (2SWS+1SWS, 6ECTS) in the Summer term 2016
Lecture: 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


Target audience:
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).


Begin:
The first lecture will be on Monday, April 11, 2016. The exercises start on Monday, April 18, 2016.

Content:

  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

Requirements:
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

Exercises:
You will find all exercise sheets on the moodle course page.

Moodle course:
There is a moodle course on which everyone should register. News and messages will be sent over this moodle platform.

Language:
The language both in the lecture and in the exercises will be English or - if preferred - German.


Literature: