Stochastic modelling and network analysis/Modélisation stochastique et analyse de réseaux

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The proposed research is composed of several ongoing projects, under the following two unifying themes. ******The main theme is mathematical modelling in situations where nonlinearity and randomness affect the behavior of large numbers of elements in an ensemble, such as the fluctuations in value of commodities on the financial markets. In the discrete case I am specifically interested in strategies leading to the reversal from a collection of losing opportunities for the client, into a winning portfolio through the use of techniques giving rise to the phenomenon called Parrondo's paradox. In the continuous case, nonlinear stochastic partial differential equations (or some associated discrete approximation scheme) in the guise of well-posed martingale problems need to be built, simulated and analyzed via interacting particle systems. My objective for the years to come is the pursuit of my ongoing research projects on the fundamental properties of these systems, which bear potential significance as they extend the applicability of classical limit theory to new mathematical contexts. ******The complementary theme is statistical modelling in the context of knowledge discovery and data mining within certain big data bases, notably heterogeneous information networks of multi-modal data such as social media networks. These require the identification of those mathematical characteristics that best suit a framework of multiple comparisons for the purpose of link prediction and community detection. I plan to incorporate hierarchical structures in the estimation methodology specifically destined for these databases. The novelty here comes from the proposal of new solutions to these issues using advanced data mining and analysis techniques, including formal concept analysis.***********