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

美法随机偏微分方程合作研究：近似和渐近分析

• 批准号: 9116174
• 负责人: Peter Li
• 金额: $ 2.01万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-04-15 至 1996-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9116174&HistoricalAwards=false
• 关键词: U.S.; France; Cooperative; Research; Stochastic

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.

这项为期三年的奖项将支持加州大学欧文分校的雷内·A·卡莫纳和巴黎理工学院应用数学中心的让-皮埃尔·福克之间的合作研究。巴黎X大学的Jean Lacroix和马赛普罗旺斯大学的Etienne Pardoux也是法国队的一员。研究人员将研究一些随机偏微分方程解的概率性质和渐近行为。他们将考虑对海洋学中的数学模型很重要的方程。卡莫纳博士是随机偏微分方程领域的领军人物。与法国调查人员的合作将加强该项目的不同方面。J.P.福克是偏微分方程方面的专家，拉克洛瓦在卢亚普诺夫指数理论、编程和随机模拟方面经验丰富。它们各自的背景将有助于解决这些方程的渐近性质问题。帕杜克斯对海洋学中的数学问题感兴趣，也有经验。他将为这一领域的数学模型的发展做出贡献。将这些互补的优势和利益结合起来将使该项目受益。这些结果将促进我们对随机偏微分方程组理论的理解，这是现代统计和概率论中一个重要而活跃的领域。