Universität Duisburg-Essen

Fakultät für Mathematik, Campus Essen

Prof. Martin Hutzenthaler; (martin (dot) hutzenthaler 'at' due (dot)de)

Master Seminar (2SWS, 9ECTS)
in the
winter term 2017/18

**Selected results on stochastic differential equations**

*Schedule:*

We will meet on Thursday, October 12, 2017 at 12:15 in WSC-S-U-3.01 and distribute talks and settle the schedule.
In addition, interested students may come to my office on Thursday, September 28, 2017 at 15:00 for discussing
questions and interests regarding talks.
The format of the seminar will be either weekly or a block seminar at the end of the semester.

*Contents:*

Students will learn about the
major progress in the literature on numerical approximations of stochastic differential equations in recent years.
We will discuss the following papers:

- The multilevel Monte Carlo method (MLMC) improves the convergence rate from 1/3 to 1/2: Giles 2008
- The stochastic Euler scheme does typically not fulfill the assumptions of the MLMC method: Hutzenthaler, Jentzen and Kloeden 2011
- A suitably tamed version of the stochastic Euler scheme typically fulfills the assumptions of the MLMC method: Hutzenthaler, Jentzen and Kloeden 2012
- Further taming methods will be discussed.

*How many credits do I get?*

You get 9ECTS as Master Seminar

*Requirements:*

Students are required to be familiar with the contents of the lecture 'Probability theory II'.

*Language:*

The language of the seminar will be English.