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

Master Seminar: Gaussian approximations with Malliavin calculus

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.

Tentative Schedule:

  1. 18.10.2016; Introduction in the topic and organization of the presentations
  2. 25.10.2016; Breuer-Major theorem, Anita Winter
  3. 06.12.2016; Universality of Wiener Chaos, Geronimo Rojas Barragan
  4. 13.12.2016; Stein's method, Kristin Schmidt
  5. 20.12.2016; Malliavin calculus in a nutshell, Anselm Hudde
  6. 10. 01.2017; Stein meets Malliavin, Arne Dilling
  7. 17. 01.2017; The smart paths method, Lars Schymonski
  8. 24.01.2017; Cumulants on the Wiener space and a new density formula,
  9. 31.01.2017; Exact rates of convergence, Arne Dilling
  10. 07.02.2017; Fourth moment theorem, Luis Osorio

Literature:

  • Ivan Nourdin, Lectures on Gaussian approximations with Malliavin calculus, lecture notes, 2012. pdf

  • 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

    The first session will start on Tuesday, 18th of October. Anita Winter will give a short introduction and we will distribute the talks. The first student presentation will be given on Tuesday, 06th of December.