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 Betabuilding
Vrije Universteit Amsterdam
De Boelelaan 10811085
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 NavierStokes 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 largesize 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 socalled
superexponential estimate.
