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

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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.