Mathematical Sciences: Probability Theory in Infinite Dimensional Spaces with Applications

首席研究员将继续研究无限维空间中的概率，特别是在一般函数类上索引的经验过程的收敛及其在统计学中的应用。他将考虑不同极限定理的一致和普遍的函数类，参数和非参数bootstrap， U-过程和可微泛函，其总体目标是增加现代经验过程理论的适用性。他还将继续研究最大无穷可分、最大稳定过程和随机集的表征和极限理论。

The principal investigator will continue his research in probability in infinite dimensional spaces, particularly on convergence of empirical processes indexed over general classes of functions and their applications in statistics. He will consider uniform and universal classes of functions for different limit theorems, the parametric and the non-parametric bootstrap, U- processes and differentiable functionals with the general aim of increasing the applicability of modern empirical process theory. He will also continue to study the characterization and limit theory of max infinitely divisible and max stable processes, and random sets.