Mathematical Sciences: Probability in Banach Spaces

数学科学：巴纳赫空间中的概率

• 批准号: 8706285
• 负责人: Michael Marcus
• 金额: $ 5.57万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-05-15 至 1989-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8706285&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Probability; Banach; Spaces

This research will explore sample path properties of certain stochastic processes. Stochastic processes serve as models in many areas of interest such as weather, economic indices, epidemics etc. The suitability of the models for specific questions of interest depends on the sample path properties of the models themselves. The study of these properties uses highly mathematical tools. This research will study three interdependent problems. The first will compare sample path properties of stochastic processes represented as certain Fourier transforms with those of random Fourier series with independent infinitely divisible coefficients. The second problem is continuation of the study with M. Talagrand of sharp estimates for certain random stable tensor products. The third will continue to study, in association with M. Weber, the tail probability distribution of Gaussian vectors.

这项研究将探索某些随机过程的样本路径特性。 随机过程可作为许多感兴趣领域的模型，例如天气、经济指数、流行病等。模型对特定感兴趣问题的适用性取决于模型本身的样本路径属性。 对这些特性的研究使用高度数学工具。 本研究将研究三个相互依赖的问题。 第一个将比较表示为某些傅里叶变换的随机过程的样本路径属性与具有独立无限可分系数的随机傅里叶级数的样本路径属性。 第二个问题是继续与 M. Talagrand 一起研究某些随机稳定张量乘积的锐估计。 第三个将继续与 M. Weber 合作研究高斯向量的尾部概率分布。