Mathematical Sciences: 1993 Summer Research Institute: Stochastic Analysis

点击翻译按钮获取中文摘要

In recent years the stochastic point of view has achieved great prominence, both as an active area of probability theory and as a powerful tool in problems of analysis, geometry, and mathematical physics. For example, the classical Ito theory of stochastic differential equations, which defines a finite- dimensional diffusion process, already leads to many interesting connections with analysis in Euclidean space and finite-dimensional differentiable manifolds. The same stochastic differential equations can also be used to define a stochastic flow, which is a diffusion process on the group of diffeomorphisms, an infinite- dimensional space. This naturally leads to the study of other infinite-dimensional processes, especially those defined by stochastic partial differential equations. This project will support the 1993 AMS Summer Research Institute on Stochastic Analysis to be held July 11-30, 1993 at Cornell University in Ithaca, NY. This Institute is the 41st in a series designed with the purpose of bringing together a group of mathematicians interested in a particular field of mathematical research. Emphasis is placed on instruction at a very high level with seminars and lectures by distinguished mathematicians in related fields, in order to promote interaction between participants while broadening their mathematical perspectives. The goal of the Institute will be to highlight the main directions of the field through principal lectures by leaders in the following general areas: stochastic (ordinary) differential equations, applications to analysis, applications to geometry, stochastic flows, infinite dimensional problems, and stochastic partial differential equations.