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

我们建议在2008年8月11日至15日举行一次关于Malliavin微积分及其应用的CBMS会议。这次会议的计划形式包括由堪萨斯大学教授David Nualart在5天内发表的10场演讲，他以其在随机分析和Malliavin演算方面的世界级工作而闻名，4场受邀的50分钟演讲，一次面向研究生和博士后的海报会议，大量的讨论咖啡休息时间，以及大多数参与者的全国旅费报销。Malliavin微积分，或随机变分，是Wiener空间上的无限维微分学，研究Wiener泛函的结构和规律性。在这次会议上演讲的目的是介绍Malliavin微积分的主要性质，包括它在证明H“ormander定理中的应用，详细讨论它与预期随机微积分的联系，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。这些研究领域为Malliavin微积分新工具的开发提供了真正的投入。会议将向与会者提供证据，证明概率和应用数学之间的互动是双向的：除了收到问题的答案外，应用数学还为概率论、随机分析和Malliavin演算提供了大量的研究问题，推动了新的令人感兴趣的数学工具的开发，并改善了数学在普通非科学公众中的形象。在这样的会议环境下，对与会者进行曝光和教育，促进这种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.