Anis Matoussi/Université du Maine, Le Mans

The obstacle problem for quasilinear stochastic PDE's and the probabilistic interpretation of the solution via BSDE's and regular potentials

Abstract: Abstract goes here

Frédéric Klopp/ Université Paris 13:

Spectral statistics for random operators in the localized regime

Abstract: It is well known that the study of random walks or Brownian motion is strongly related to the study of random operators. In this talk, we will present recent results concerning the spectral statistics of random operators in the localized phase such as the local level distribution, the level spacing distribution, the localization center distributions, etc.

Klaus Ritter/TU Darmstadt:

Multi-level Algorithms for Infinite-dimensional Integration

Abstract: Stochastic multi-level algorithms have turned out to be a powerful tool for variance reduction in different settings. In this talk we will first introduce the multi-level idea for integration with respect to the Wiener measure, and we will point to applications for stochastic differential equations as well.

Anton Bovier/Bonn:

Metastability in Ginzburg-Landau type spdes

Abstract: We consider a coupled bistable $N$-particle system on $\R^N$ driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable states, both for fixed $N$ and in the limit when $N$ tends to infinity, with error estimates uniform in $N$. These estimates are a main step towards a rigorous understanding of the metastable behavior of infinite dimensional systems, such as the stochastically perturbed Ginzburg-Landau equation. Our results are based on the potential theoretic approach to metastability. This is based on joint work with Florent Barret and Sylvie Méléard.

Bikramjit Das/Z"urich:

Conditional extreme value limits and regular variation on cones

Abstract: Customarily multivariate extreme value theory implicitly assumes that each component of a random vector belongs to an extreme-value domain of attraction. Heffernan & Tawn (2004) and Heffernan & Resnick (2007) developed an approximation to the joint distribution of the random vector by conditioning on one of the components being in an extreme-value domain. The usual method of analysis using multivariate extreme value theory is not helpful in certain cases which we can overcome by using this conditional model. We resolve the issue of consistency of different models obtained by conditioning on different components being extreme. We also clarify the relationship between the conditional model, regular variation on cones and hidden regular variation. We propose three statistics which act as tools to detect the plausibility of using this model. llustratrations are provided with an internet traffic data example. (joint work with Sidney Resnick)

Plamen Turkedjiev/Berlin:

Numerical Methods for BSDEs with Lipschitz driver

Abstract: BSDEs is a topic that has attracted a lot of attention in the last two decades, and vigorous research has brought about large expansions in both theory and application. Being able to calculate explicit solutions of BSDEs is becoming increasingly important, and many numerical methods have been developed over the last ten years. In this talk, we look at numerical methods for BSDEs with Lipschitz drivers. In paticular, we consider approximations based on Monte Carlo methods and Picard iterations, and determine convergence of such approximations to the true solution.

No talk!