Mathematical Sciences: 1993 Summer Research Institute: Stochastic Analysis

近年来，随机的观点已经实现了 作为概率论的活跃领域， 作为一个强大的工具，在分析问题，几何， 数学物理 例如，经典的伊藤理论 随机微分方程，它定义了一个有限的， 三维扩散过程，已经导致了许多有趣的 与欧几里得空间和有限维空间中的分析的联系 微分流形 相同的随机微分 方程也可以用来定义一个随机流，这是一个 扩散过程的群的同态，一个无限的- 维度空间 这自然会导致对其他人的研究。 无限维过程，特别是那些定义为 随机偏微分方程 该项目将支持1993年AMS夏季研究 随机分析研究所将于1993年7月11日至30日在 康奈尔大学，纽约州伊萨卡。 该研究所是第41个在一个 系列设计的目的是汇集一组 对某个数学领域感兴趣的数学家 research. 重点放在教学在一个非常高的水平 与研讨会和讲座，由著名的数学家， 相关领域，以促进互动 参与者，同时扩大他们的数学观点。 的 研究所的目标将是突出主要方向， 通过以下领导人的主要讲座， 一般领域：随机（常）微分方程， 分析应用，几何应用，随机 流、无穷维问题和随机偏微分方程 微分方程

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.