U.S.-France Cooperative Research: Random Fractals, Multivariate Wiener Processes and Empirical Processes and Applications

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This three-year award for U.S.-France cooperative research in probability involves David Mason and Wenbo Li at the University of Delaware, and Paul Deheuvels and Zhan Shi at the University of Paris VI. The investigators propose to investigate several problems in the general area of limit theorems in probability. In particular, they will investigate the sample path properties of the multivariate Wiener process by studying the multi-fractal behavior of its increments and obtaining precise estimates of its small probabilities. The project takes advantage of complementary expertise of the U.S. and French investigators in Gaussian and Wiener processes and on the path properties of Brownian and iterated Brownian motion. The proposal will advance fundamental understanding of limit theorems and their applications to other areas of probability.