Mathematical Sciences: Regular Variation: Analytic Approaches to Probability and Statistics

正则变分的数学分析概念是研究和极值的基础。这项研究将探讨这一分析分支在概率统计中更广泛的主题中的应用，特别是在无限可分分布和Levy过程、非参数函数估计、变量的长期相关性以及具有无穷大方差和/或大偏差的回归问题中的应用。多元次指数，一个相关的概念，将被研究，因为它与极值和随机变量和的尾部行为有关。

The mathematical analytic concept of regular variation is fundamental for the study of sums and of extremes. This research will investigate the applications of this branch of analysis to a wider range of topics in probability and statistics, particularly to infinitely divisible distributions and Levy processes, to nonparametric function estimation, to long-range dependence of variables, and to regression problems with infinite variance and/or large deviations. Multivariate subexponentiality, a related concept, will be studied as it relates to tail-behavior of extremes and of sums of random variables.