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Abstract

The OMEGA project is located at two sites: Sophia Antipolis and Nancy.

The objective of this project is to develop and analyze probabilistic numerical methods. Two fields of applications are emphasized: the numerical resolution of Partial Differential Equations (in particular those in Fluid Mechanics and in Neutronics) and the calculation of complex quantities arising in Financial Mathematics.

In 1996 the research themes of OMEGA have been:

• the simulation of the distributions of stochastic processes and the study of discretized stochastic differential equations;
• the development and analysis of probabilistic numerical methods (and in particular Monte Carlo methods and methods of stochastic particle systems);
• estimates on the speed of convergence of the methods;
• the probabilistic interpretation of various nonlinear PDE's in terms of the limit laws of particle systems;
• construction of models for the stock market and related objects in Financial Mathematics; study of computational problems arising in Insurance and Accounting; and the numerical calculation of complex prices of financial derivatives (e.g., stock options);
• computations performed on computers using parallel architecture.