Précédent : Références Remonter : Projet SYSDYS

Abstract

The SYSDYS project aims at developing numerical probability methods. Its main competence fields are stochastic differential equations, partial differential equations with random coefficients and finally stochastic partial differential equations.

SYSDYS is a common project INRIA Sophia Antipolis, the LATP (CNRS ) and the University of Provence. It is located in the ``Technopôle'' of Château Gombert in Marseilles.

In 1996, SYSDYS's activities were :

Homogenization in random media : This is the main activity of the group. We investigated many problems : homogenization of PDE 's linked with BSDE (backward stochastic differential equations), homogenization and Dirichlet forms, limiting behavior of the effective diffusion for two-component random difference operators, boundary homogenization in the domains with very rapidly oscillating boundary. We also focused on numerical methods : approximation of effective coefficient by means of random walks.

Backward stochastic differential equations (BSDE ) : We improved results concerning solutions of BSDE 's and extended the class of PDE 's which admit a probabilistic interpretation by means of such processes.

Equilibrium statistical mechanics : We proposed rigorous results for the analysis of the classical Heisenberg model with long range interactions.

Scientific collaborations  : Random media: University of Provence, Princeton University, Moscow State University. Non linear identification: IRISA, University of Southern California, Rutgers University.

Contracts  : IFP : reservoir engineering. HCM ``System Identification''. HCM ``Statistical inference for stochastic processes''. ONR ``Numerics for non linear filtering''.