Houdré's main current interest has to do with sequence comparison.
He is fascinated by various problems
arising in
computational genetics and computational linguistics.
These problems
involve a lot of deep mathematics
and have connections to various
subfields such as algebraic combinatorics and random matrices.
Among his ultimate goals is the development of quantitative and statistical techniques
in sequence comparison.
Over the years, he has been interested in
isoperimetric and functional inequalities to obtain
probabilistic "large deviations" estimates for functions
of multivariate vectors.
This work was done in various frameworks, from metric spaces to
graphs and Markov chains, leading to
spectral gap and log-Sobolev estimates useful in
Combinatorics, Statistical Physics and
Theoretical Computer Science.
More recently, his interests have been
towards obtaining such results
for the important class of
infinitely divisible random vectors.
He is also interested in nonstationary stochastic
processes (representation,
prediction, filtering,
wavelet transform,...)
and some aspects of Lévy processes.
His research in Mathematical Finance has
mainly to do with
understanding how
classical
Brownian models can be
extended to more realistic
situations containing jumps.
His statistical interests are mainly in non-parametric estimation.
Past projects involved the use
of wavelet methods in Statistics
while a more recent one deals with the estimation of Lévy
measures
motivated by Mathematical Finance. In that context, his work on concentration
inequalities
for infinitely divisible laws appear to be quite useful.
He has also interacted with various individuals
on applied research projects, where stochastics tools
were needed, in
Aerospace Engineering, Biology,
Chemistry and Electrical Engineering all of it at Georgia Tech.
Finally, he is on the editorial board of The IMS Lecture Notes-Monograph Series,
The IMS Collections ,
The Journal of
Fourier Analysis and Applications and
of The
Journal of Computational Analysis and Applications.