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.
