Mathematical Sciences: Probability in Banach Spaces

本研究将探讨某些随机过程的样本路径性质。随机过程在天气、经济指数、流行病等许多感兴趣的领域中充当模型。模型对感兴趣的特定问题的适用性取决于模型本身的样本路径属性。对这些性质的研究使用高度数学化的工具。本研究将研究三个相互依存的问题。第一部分将比较用特定傅里叶变换表示的随机过程的样本路径性质与具有独立无限可分系数的随机傅里叶级数的样本路径性质。第二个问题是对M. Talagrand关于某些随机稳定张量积尖锐估计的研究的延续。第三位将与韦伯先生一起继续研究高斯矢量的尾部概率分布。

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.