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

这项为期三年的奖项将支持合作研究， Rene A.加州大学欧文分校的卡莫纳和 让-皮埃尔·福克（Jean-Pierre Fouque），应用数学中心， 巴黎的理工学院。 让·拉克鲁瓦， 巴黎十世和普罗旺斯大学的艾蒂安·帕杜 马赛也是法国队的一员。 调查人员将 研究的概率性质和渐近行为 一些随机偏微分方程的解。 他们 我会考虑对数学模型很重要的方程 在海洋学中。 卡莫纳博士是随机偏微分领域的领导者 方程 与法国调查人员的合作将 加强这个项目的各个方面。 J·P·福克是一位 关于偏微分方程和拉克鲁瓦的经验 Luyapunov指数理论、规划与随机 仿真 他们各自的背景将有助于解决 这些方程的渐近性质的问题。帕尔杜 对数学问题有兴趣和经验， 海洋学 他将为发展 数学模型在这个领域 结合这些互补 优势和利益将有利于项目。 结果将 提高了我们对随机偏微分方程理论的认识 微分方程是现代数学中一个重要而活跃的领域， 统计与概率论

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.