Mathematical Sciences: Probability Theory in Infinite Dimensional Spaces with Applications

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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.