Mathematical Sciences: Probability in Banach Spaces

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This research will explore sample path properties of certain stochastic processes. Stochastic processes serve as models in many areas of interest such as weather, economic indices, epidemics etc. The suitability of the models for specific questions of interest depends on the sample path properties of the models themselves. The study of these properties uses highly mathematical tools. This research will study three interdependent problems. The first will compare sample path properties of stochastic processes represented as certain Fourier transforms with those of random Fourier series with independent infinitely divisible coefficients. The second problem is continuation of the study with M. Talagrand of sharp estimates for certain random stable tensor products. The third will continue to study, in association with M. Weber, the tail probability distribution of Gaussian vectors.