This "research opportunities for women" project will consider uniform central limit theorems for families of semi- martingales. These arise as the extensions of the results in empirical processes for independent identically distributed random variables. The principal investigator has already found sharpest results so far in the traditional empirical processes area using the "bracketing" technique. The relaxation of the condition of independence makes the theory open to wider applications. The particular dependence structure assumed here is that of semi-martingales. One of the anticipated applications is to provide approximations to certain self-similar Gaussian random fields which arise in modeling physical variation.
