U.S.-France Collaborative Research (INRIA): Numerical Analysis of Stochastic Differential Equations

9401108 Protter这项为期三年的持续拨款支持美国和法国在随机微分方程（SDE）数值分析方面的合作研究。研究人员是普渡大学的Philip Protter，威斯康星大学的Thomas Kurtz，法国国家计算机科学与应用数学研究所的Denis Talay和巴黎第六大学的Jean Jacod。研究人员确定了六个探索主题，包括随机微分方程离散化及其流动的研究；抛物型偏微分方程数值分析及数学金融学的应用以及相互作用粒子系统的数值分析。随机微分方程处理随机动力系统的建模，并已应用于统计通信理论，金融理论，控制理论等模型。随着计算机的出现，现在对这些模型进行数值分析是很重要的。该项目利用了INRIA研究人员的独特专业知识，他们在随机微分方程方面处于世界领先地位。这项工作的结果将进一步理解其他数值问题，并促进我们对随机微分方程的特殊性的理解。例如，SDEs最终可能会用更高效、更快的计算模型取代当前的金融模型。＊＊＊

9401108 Protter This three-year continuing grant supports U.S.-France cooperative research in numerical analysis of stochastic differential equations (SDE). The investigators are Philip Protter of Purdue University, Thomas Kurtz of the University of Wisconsin, Denis Talay, French National Institute for Research in Computer Science and Applied Mathematics and Jean Jacod, University of Paris VI. The investigators have identified six topics for exploration, including studies of the discretization of stochastic differential equations and their flows; applications to numerical analysis of parabolic partial differential equations and to mathematical finance; and numerical analysis of interacting particle systems. Stochastic differential equations deal with the modeling of random dynamical systems and have been applied to models for statistical communication theory, finance theory, control theory among others. With the advent of computers, it is now important to analyze such models numerically. The project takes advantage of unique expertise of the INRIA researchers, who are world leaders in stochastic differential equations. The results of this work will further understanding of other numerical problems and advance our understanding of the special nature of stochastic differential equations. SDEs could eventually replace, for example, current financial models with more efficient and faster computational models. ***