NSF/CBMS Regional Conference in Mathematical Sciences - Malliavin Calculus and its Applications - Summer 2008

我们建议在2008年8月11-15日召开一次关于Malliavin微积分及其应用的CBMS会议。本次会议的计划形式包括由堪萨斯大学教授David Nualart在5天内进行的10场讲座，他以其在随机分析和Malliavin微积分方面的世界级工作而闻名，4场50分钟的受邀演讲，一次面向研究生和博士后的海报会议，大量的咖啡休息时间用于讨论，以及大多数参与者的全国旅行报销。Malliavin微积分，或随机变分微积分，是一种在维纳空间上的无限维微分微积分，研究维纳泛函的结构和规律性。本次会议演讲的目的是介绍Malliavin微积分的主要性质，包括它在H\ ormander定理证明中的应用，详细讨论它与预测随机微积分的联系，并介绍它在扩散理论、金融数学、随机控制、投资组合优化、排队和数学物理中的几个应用。这些领域的研究提供了一个真正的输入，以发展新的工具，在马利亚文微积分。会议将向与会者提供证据，证明概率论与应用数学之间的互动是双向的：除了获得问题的答案外，应用数学还为概率论、随机分析和马利亚文微积分提供了大量的研究问题，激发了人们内在兴趣的新数学工具的发展，并改善了数学在一般非科学公众中的形象。在这样的会议环境中，对与会者进行宣传和教育，促进这些思想的交流是最合适的。

We propose a CBMS conference on Malliavin Calculus and its Applications, to be held on August 11-15, 2008. The planned format for this conference includes 10 lectures delivered over 5 days by David Nualart, Professor at Kansas University, well known for its world-class work in stochastic analysis and Malliavin calculus, 4 invited 50-minute talks, one poster session for graduate students and postdocs, plenty of coffee breaks for discussions, and nationwide travel reimbursement for most participants.The Malliavin calculus, or stochastic calculus of variations, is an infinite-dimensional differential calculus on the Wiener space, investigating the structure and regularity of Wiener functionals. The purpose of the lectures delivered during this conference is to present the main properties of Malliavin calculus, including its application to the proof of H\"ormander's theorem, to discuss in detail its connection with the anticipating stochastic calculus and to present several of its applications to diffusion theory, financial mathematics, stochastic control, portfolio optimization, queueing, and mathematical physics. These fields of research provide a real input to the development of new tools in Malliavin calculus. The conference will provide evidence to the participants that the interaction between Probability and Applied Mathematics is bidirectional: beyond receiving answers to its questions, Applied Mathematics provides great research problems for probability theory, stochastic analysis and Malliavin calculus, motivates the development of new mathematical tools of intrinsic interest, and improves the image of Mathematics with the general non-scientific public. Exposing and educating the participants, facilitating the exchange of such ideas are most appropriate in such a conference setting.