Mathematical Sciences: Random Multilinear Forms and MultipleStochastic Integrals

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The aim of the researchers is to study multiple stochastic integrals and multilinear random forms. A general stochastic integral of functions of multiple variables with respect to multidimensional stochastic processes is a random variable. The major goals of the research are to find the class of integrable functions and to study the distributional properties of the integral. A major technique in studying these integrals is the decoupling inequality. The investigators have already done work in this area. They will continue to extend the known decoupling techniques. They will also study the applicability of the hyper- contraction principle and resulting comparison theorems.