Several Questions in Probability Theory

概率论中的几个问题

• 批准号: 9971146
• 负责人: Theodore Hill
• 金额: $ 7万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971146&HistoricalAwards=false
• 关键词: Several; Questions; Probability; Theory

The principal investigator is carrying out research on topics related to the mathematical theory of probability. Specific objectives include continuation of his investigations of optimal-stopping problems (especially stopping under incomplete information), constructions of random distributions, analysis and applications of Benford's law, general partitioning inequalities, and convergence and invariance principles. In new directions he is studying sharp inequalities for expected extrema and general continuity-representation theorems. The research has both theoretical and applied components, and involves collaboration with other researchers both at Georgia Tech and other universities, as well as with several graduate students. This research involves the study of random processes, such as evolving financial markets or government policies, when unpredictable fluctuations are present. Much is known if there is complete knowledge of the nature of the random fluctuations, but this is usually not the case in practice. One of the thrusts of this research is to try to discover good methods for deciding when to stop or change a policy when only partial information is available about the random fluctuations. Another thrust of this research is to develop new statistical tools for estimating changes in random processes. One very new use of these ideas is application to detection of fraud in financial data. The idea is that fabricated data is usually qualitatively different from true data, and there are just recently tests based on these fluctuation theories which are proving useful in distinguishing true from fabricated data. Applications of the research on random measures includes new models for the distribution of mass in space, including various settings in physics and materials science.

主要研究者正在进行与概率数学理论相关的课题研究。具体目标包括继续他的调查最优停止问题（特别是停止在不完全信息），建设随机分布，分析和应用本福德定律，一般分割不等式，收敛和不变性原则。在新的方向，他正在研究尖锐的不平等预期极值和一般连续性表示定理。这项研究既有理论和应用的组成部分，并涉及与其他研究人员都在格鲁吉亚理工学院和其他大学，以及与几个研究生的合作。该研究涉及随机过程的研究，如金融市场或政府政策的演变，当不可预测的波动存在。如果对随机波动的性质有完全的了解，那么我们就知道了很多，但实际情况通常并非如此。本研究的重点之一是试图找到在仅获得有关随机波动的部分信息时决定何时停止或改变政策的好方法。这项研究的另一个重点是开发新的统计工具来估计随机过程的变化。这些想法的一个非常新的用途是应用于金融数据中的欺诈检测。这个想法是，捏造的数据通常与真实数据有本质上的不同，最近才有基于这些波动理论的测试，这些测试被证明有助于区分真实数据和捏造数据。随机测量研究的应用包括空间质量分布的新模型，包括物理学和材料科学中的各种设置。