Mathematical Sciences: Random Multilinear Forms and MultipleStochastic Integrals

研究人员的目标是研究多重随机积分和多线性随机形式。多元函数关于多维随机过程的一般随机积分是随机变量。研究的主要目的是找出可积函数类，并研究积分的分布性质。研究这些积分的一个主要方法是解耦不等式。调查人员已经在这一领域做了工作。他们将继续推广已知的脱钩技术。他们还将研究超压缩原理和由此产生的比较定理的适用性。

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.