Research Interests

Since I started doing research, I have been interested in several subjects within probability and stochastic analysis. I have mainly studied stochastic partial differential equations (SPDEs), nonlinear filtering, Lyapounov exponents of bilinear stochastic differential equations, anticipating stochastic calculus, backward stochastic differential equations and homogenization of partial diferential equation by probabilistic methods. I worked on SPDEs during several distinct periods, using a variety of tools and techniques. Most of those are exposed in the notes of a series of lectured delivered successively in Lausanne, Zanjan and Shanghai. Those notes are available on this WEB site.
A few years ago, I turned my interests towards probabilistic models for evolutionnary biology and population genetics. The probabilistic models which I am studying with my collaborators and my Phd students include models of random trees, the coalescent with recombinations, models of genetic hitch-hiking produced by a selective sweep, etc. I am also interested, in collaboration with Pierre Pontarotti and young Colleagues in using those models in order to analyse data in order for example to reconstruct ancestral genomes, detect horizontal gene transfers, etc.