U.S.-France Cooperative Research on Stochastic Partial Differential Equations: Approximations and Asymptotic Analysis

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This three-year award will support cooperative research between Rene A. Carmona of the University of California at Irvine and Jean-Pierre Fouque, of the Center of Applied Mathematics at the Ecole Polytechnique in Paris. Jean Lacroix of the University of Paris X and Etienne Pardoux of the University of Provence in Marseille are also part of the French team. The investigators will examine the probabilistic properties and the asymptotic behavior of the solutions of some stochastic partial differential equations. They will consider equations which are important to mathematical models in oceanography. Dr. Carmona is a leader in the field of stochastic partial differential equations. Collaboration with the French investigators will enhance different aspects of this project. J.P. Fouque is an expert on partial differential equations and Lacrois is experienced in the theory of Luyapunov exponents, programming and random simulation. Their respective backgrounds will contribute to solving problems on the asymptotic properties of these equations. Pardoux has interest and experience in mathematical problems in oceanography. He will contribute to the development of mathematical models in this area. Combining these complementary strengths and interests will benefit the project. The results will advance our understanding of the theory of stochastic partial differential equations, an important and active area in the modern theory of statistics and probability.