Stochastic integration is a very useful analytic tool in applications of many models to real life. In recent years, the classical theory of stochastic integration has been generalized to other cases. This makes it possible to use more general models. This research will continue to study stochastic integration with the help of some special techniques called the decoupling inequalities. In the standard setting of a stochastic integral, the integrant and the integrating stochastic process are independent. Decoupling inequalities mainly try to handle the lack of such independence by separating the independent part and bounding the remaining part. This research will study stochastic integration with respect to infinite dimensional stochastic processes with the help of the decoupling inequalities. It will also study the applications to U-statistics.
