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

NSF/CBMS 数学科学区域会议 - Malliavin 微积分及其应用 - 2008 年夏季

• 批准号: 0735352
• 负责人: Oana Mocioalca
• 金额: $ 3.57万
• 依托单位: Kent State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-05-01 至 2009-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0735352&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

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.

我们建议CBMS会议Malliavin演算及其应用，将于2008年8月11日至15日举行。本次会议的计划形式包括由堪萨斯大学教授大卫Nualart在5天内提供的10个讲座，该大学以其在随机分析和Malliavin演算方面的世界级工作而闻名，4个50分钟的邀请演讲，一个针对研究生和博士后的海报会议，大量的咖啡休息时间进行讨论，以及大多数参与者的全国旅行报销。随机变分法（英语：Stochastic calculus of variations），是一种在维纳空间上的无穷维微分学，研究维纳泛函的结构和正则性。在这次会议期间提供的讲座的目的是目前的Malliavin演算的主要属性，包括其应用的H\“Ormander定理的证明，详细讨论其与预期的随机微积分的连接，并提出几个其应用扩散理论，金融数学，随机控制，投资组合优化，投机，和数学物理。这些领域的研究提供了一个真实的输入Malliavin演算的新工具的发展。 会议将向与会者提供证据，证明概率和应用数学之间的相互作用是双向的：除了接收问题的答案，应用数学为概率论，随机分析和Malliavin演算提供了很大的研究问题，激发了固有兴趣的新数学工具的发展，并改善了数学与一般非科学公众的形象。在这样的会议环境中，向与会者展示和教育，促进这种想法的交流是最合适的。