Mathematical Sciences: Norming Operators for Generalized Domains of Attraction

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The central limit theorem is the most fundamental result in mathematical statistics. It states that the partial sums of a sequence of independent identically distributed random variables with finite variance can be normalized so that they converge in distribution to a normal law. In the case of infinite variance, convergence is still possible, and the limit is either normal or a nonnormal stable law. For random vectors it is known that similar results hold, but there does not yet exist a practical method for construction of the norming operators. The principal investigator intends to develop such a method. This work will bring the existing theoretical results on multivariable generalizations of the central limit theorem one step closer to practical applications. The principal investigator will work in the area of mathematics concerning limits of random vectors. This research is in the center of the field of probability and mathematical statistics. The principal investigator is working at a small, liberal arts college, and this award is being made via the Research in Undergraduate Institutions program.