Mathematical Sciences: Problems in the Theories of Partial Sums, Self-Normalized Sums, Partial Maxima and Random Sets

首席研究员将研究涉及概率理论各个分支的问题，包括经典的独立随机变量部分和理论、巴纳赫空间中的概率和随机集理论。主要目的是澄清和扩展对三个相关的概率主题的理解，这些主题既有理论意义又有应用价值：1)近似独立实值随机向量及其伴随的自归一化和的和的分布；2)独立同分布样本连续过程的偏极大值渐近理论；3)独立或依赖随机集和增长模型的并集。前两个主题对统计学有潜在的应用，而第三个主题对生物学有潜在的应用。这项工作将与合作者一起进行。

The principal investigator will conduct research on problems which intersect various branches of probability theory including the classical theory of partial sums of independent random variables, probability in Banach spaces and the theory of random sets. The major objective is to clarify and extend the understanding of three related probabilistic topics which are of both theoretical and applied interest: 1) approximate the distribution of sums of independent real valued random vectors and their accompanying self-normalized sums; 2) asymptotic theory of partial maxima of independent and identically distributed sample continuous processes; 3) unions of independent or dependent random sets and models for growth. The first two topics have potential applications to statistics, while the third topic has potential applications to biology. The work will be conducted with collaborators.