Questions in Probability Related to Isoperimetry and Random Fourier Series

与等周法和随机傅里叶级数相关的概率问题

• 批准号: 9803239
• 负责人: Christian Houdre
• 金额: $ 2.62万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803239&HistoricalAwards=false
• 关键词: Questions; Probability; Related; Isoperimetry; Random

9803239HoudreProfessor Houdre is investigating various topics in probability and statistics. His theoretical work includes isoperimetric problems for product probability measures, graphs and Markov chains, jackknife based deviation inequalities and new directions in the study of random Fourier series. His applied projects include studying the probability of error in biostatistical modeling as well as the application of deviation inequalities in aerospace engineering.Professor Houdre's work in bioinformatics addresses questions of error inherent in popular genome sequencing algorithms which were used in the mapping of E. Coli and more recently, H. Pylori. His work in aerospace engineering involves the application of stochastic algorithms to the design of high speed civil transportation aircraft. The theoretical underpinnings of these applied activities will also be advanced since isoperimetric methods often provide good estimates of probability distributions which have a tremendous number of applications. In particular, Professor Houdre will continue to bridge modern statistical resampling methods and distribution estimates for general classes of statistics. Finally his work on random Fourier series will provide tools and methods for the analysis of fractal-like physical phenomena.

9803239Houdre Houdre 教授正在研究概率和统计方面的各种主题。 他的理论工作包括产品概率测度的等周问题、图和马尔可夫链、基于折刀的偏差不等式以及随机傅立叶级数研究的新方向。 他的应用项目包括研究生物统计建模中的错误概率以及偏差不等式在航空航天工程中的应用。Houdre 教授在生物信息学方面的工作解决了流行的基因组测序算法中固有的错误问题，这些算法被用于绘制大肠杆菌和最近的幽门螺杆菌图谱。 他在航空航天工程方面的工作涉及随机算法在高速民用运输飞机设计中的应用。 这些应用活动的理论基础也将得到推进，因为等周方法通常可以提供具有大量应用的概率分布的良好估计。 特别是，Houdre 教授将继续将现代统计重采样方法和一般统计类别的分布估计联系起来。最后，他在随机傅里叶级数方面的工作将为分析分形物理现象提供工具和方法。