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).


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

Content:

  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

Requirements:
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

Exercises:
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.


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

Literature: