Universität Duisburg-Essen

Fachbereich Mathematik

Geronimo Rojas Barragan und Anita Winter

6th October 2016

Master Seminar (2SWS)

Winter Semester 2016/17

Tuesday, 14.15-15.45; WSC-S-U-3.03

In this seminar we are going to present all technical tool needed to prove the surprising Fourth Moment Theorem. This is a central limit theorem for a sequence of stochastic integrals of a fixed order: in this context convergence in distribution to the standard normal distribution is equivalent to convergence of just the fourth moment.
Winter Semester 2016/17

Tuesday, 14.15-15.45; WSC-S-U-3.03

**Master Seminar: Gaussian approximations with Malliavin calculus**

*Tentative Schedule:*

- 18.10.2016; Introduction in the topic and organization of the presentations
- 25.10.2016; Breuer-Major theorem, Anita Winter
- 06.12.2016; Universality of Wiener Chaos, Geronimo Rojas Barragan
- 13.12.2016; Stein's method, Kristin Schmidt
- 20.12.2016; Malliavin calculus in a nutshell, Anselm Hudde
- 10. 01.2017; Stein meets Malliavin, Arne Dilling
- 17. 01.2017; The smart paths method, Lars Schymonski
- 24.01.2017; Cumulants on the Wiener space and a new density formula,
- 31.01.2017; Exact rates of convergence, Arne Dilling
- 07.02.2017; Fourth moment theorem, Luis Osorio

*Literature:*

*What should I know if I want to participate?*

The seminar is offered as part of the Master Program in Mathematics.
Nevertheless, if you are interested in probability theory you are very welcome to participate and contribute with a presentation. Preknowledge is the course Probability Theory II (Wahrscheinlichkeitsthoerie II).
Don't hesitate to send me an e-mail for more information:

anita(dot)winter `at' due(dot)de