EMSW21-RTG: Training, Mentoring & Research in the Mathematics of Stochastic Analysis and Applications

EMSW21-RTG：培训、指导

• 批准号: 0739195
• 负责人: Rene Carmona
• 金额: $ 226.88万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-02-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0739195&HistoricalAwards=false
• 关键词: EMSW21; RTG; Training; Mentoring; &amp

This project is concerned with the research and teaching of themathematics of stochastic analysis, motivated by a number of timelyapplication areas. These applications, among them financialmathematics, telecommunications, risk measure analysis, dynamicalqueuing systems, and green-house gas emissions, are key to attractingyoung talent towards stochastic analysis, which is an area that hasbeen rewarded with a number of major mathematical prizes in the pasttwo years. Some of the technical issues arising from the problemsstudied here are: analysis of very heavy tailed distributions;stochastic partial differential equations; multiscale asymptoticapproximations for jump processes; convex analysis for set-valuedfunctions; limit theorems for time-changed Poisson process models ofMarkovian service networks. Tools of stochastic analysis are becomingcrucial for a core applied mathematics training, and this RTG aims totrain a number of the future trainers, as well as practitioners of theskills, with rigorous foundations in this area.Expertise in probability, the mathematics of uncertainty, is in greatdemand in the US: university mathematics departments and appliedmathematics programs, operation and risk management, financialregulatory and public policy offices, bio-engineering, and thetelecommunications industry. The initiatives of this project aredesigned to attract talented US students to graduate degrees, as wellas postdoc positions and beyond. The RTG's educational emphasis onmathematical methodology means that we will train people with broadlyapplicable technical skills that may later be applied in vastlydifferent contexts as demands and trends in the workplace evolve. Infinancial markets, for example, poor regulation and a lack ofunderstanding of the risks involved, have contributed to wide-rangingcrises, such as that triggered by the subprime mortgage debacle inSummer 2007, threatening more and more retirement and endowment fundsand public savings every day. We need to stop this run-away train. Anultimate goal of this project is to contribute to this effort bydeveloping new tools and strategies to educate the future scientists,policy makers and regulators, and potential investors about the risksand the mathematical language for their description and control. Byfocusing on forms of risk which have traditionally remained off theradar screen of educators and practitioners, e.g. operational risk, wewill raise the level of awareness and make sound controls possible.

该项目涉及由许多及时申请领域的随机分析的研究和教学。这些应用，包括金融音乐，电信，风险措施分析，动力学系统和绿色房屋气体排放，是吸引Young的才华进入随机分析的关键，在过去的年份中，这是一个在过去的几年中获得许多重大数学奖品的领域。此处研究的问题引起的一些技术问题是：分析非常重的尾部分布；随机偏微分方程；跳跃过程的多尺度渐近应用；集合功能函数的凸分析；限制定理的定理，以限定时间变化的泊松过程模型。 随机分析的工具对于核心应用数学培训而变得重要，该RTG旨在使许多未来的培训师以及这些领域的实践者在该领域中具有严格的基础。在可能的情况下，不确定性的数学是在此领域的概述，在使用中的数学策略和应用程序的运作范围是：办公室，生物工程和Thetelecommunications行业。该项目的举措旨在吸引有才华的美国学生登上研究生学位，以及韦拉斯博士后及其他职位。 RTG的教育强调上学方法论意味着，我们将培训具有广泛适用技术技能的人，随着工作场所的需求和趋势的发展，后来可以在大致不同的环境中应用。例如，无财务市场的监管差，缺乏对所涉及的风险的理解，这导致了广泛的危险，例如由次级抵押贷款损失Insummer 2007触发的，威胁到越来越多的退休，退休和捐赠基金和每天的公众储蓄。我们需要停止这台失败的火车。该项目的极斗目标是为这项努力做出援助YENEDENDE YEARD的新工具和策略，以教育未来的科学家，政策制定者和监管机构，以及潜在的投资者有关风险和数学语言的描述和控制。传统上仍在教育工作者和从业人员的Theradar屏幕上旁观的风险形式，例如操作风险，我们将提高意识水平，并使声音控制成为可能。