On Thursday March 5, 2009 there was a Stieltjes afternoon at the Vrije Universteit Amsterdam, organized by the Thomas Stieltjes Institute for Mathematics.

During the meeting the Rector of the Vrije Universiteit Amsterdam has presented the Stieltjes Prize for the best Ph.D. thesis in 2007 to Dr. Jasper Anderluh, who has given a presentation on his thesis work.

After that there were 3 presentations on the work of S.R.S. Varadhan (Courant Institute, New York), who was awarded the Abelprize 2007 by the Norwegian Academy of Sciences "for his fundamental contributions to probability theory".

PROGRAMME

13:30 -- 13:45
Presentation of the Stieltjes Ph.D.-student prize by Prof.dr.Lex Bouter,
Rector Magnificus Vrije Universteit Amsterdam.

13:45 -- 14:15
Dr. Jasper Anderluh, HiQ Invest en Technische Universiteit Delft
" Probabilistic methods in exotic option pricing".
text of this presentation

14:15 -- 14:45
Prof.dr. Frank den Hollander, Universiteit Leiden en EURANDOM,
"Large Deviations"
text of this presentation

14:45 -- 15:15
BREAK

15:15 -- 15:45
Prof.dr. Jan van Neerven, Technische Universiteit Delft,
"Martingales methods in the theory of SDE".
text of this presentation

15:45 -- 16:15
Dr. Frank Redig, Universiteit Leiden,
"Hydrodynamic limits and large deviations".

16:15 --17:15
DRINKS

Location:
room: KC 159 in the Beta-building
Vrije Universteit Amsterdam
De Boelelaan 1081-1085
1081 HV Amsterdam

ABSTRACTS

"Large Deviations" (Frank den Hollander).
On 22 March 2007, S.R.S. Varadhan was awarded the Abelprize 2007 "for his fundamental contributions to probability theory and, in particular, for his creation of a unified theory of large deviations". In this talk I will give an overview of the main ingredients of Varadhan's large deviation theory, which describes atypical behavior in random processes. These ingredients will be placed in a historical context, and a few key applications will be mentioned as well.

"Martingales methods in the theory of SDE" (Jan van Neerven).
In joint work with D.W. Stroock, the 2007 Abel Prize recipient S.R.S. Varadhan developed a powerful approach based on martingale methods for solving stochastic differential equations under very general assumptions on the coefficients. In this talk we discuss this method and place it into a historical context.

"Hydrodynamic limits and large deviations" (Frank Redig).
How to derive hydrodynamic equations, such as the Euler equation, the diffusion equation or the Navier-Stokes equation, starting from the microscopic motion of atoms, is a key problem of statistical mechanics. In simplified stochastic models of atomic motion, such as lattice gases, hydrodynamic equations appear as a consequence of the law of large numbers. Therefore it is natural to ask for the probability that a large-size system follows a trajectory that deviates from the solution of the hydrodynamic equations. In the context of diffusion processes, Guo, Papanicolaou and Varadhan, and later in the context of lattice gases, Kipnis, Olla and Varadhan answered this question. I will explain their ingenious and elegant technique, based on a so-called superexponential estimate.