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

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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. ***