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

正则变分的数学分析概念是 是研究求和和极值的基础。 本研究 我将研究这一分析分支的应用， 在概率和统计的更广泛的主题，特别是 无限可分分布和Levy过程， 非参数函数估计，对 变量，以及具有无穷方差的回归问题 和/或大偏差。 多元次指数性，a 相关的概念，将研究，因为它涉及到尾部的行为 极值和随机变量之和的概率。

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.