Our main goal is to develop a theory of stochastic integration with respect to cylindrical martingalevalued measures defined on Banach spaces.

The main objective is to establish sparse bilinear bounds for singular integral operators in a discrete setting, with the purpose of obtaining more general vector valued inequalities and weighted L^p estimates.

In this project we study properties of cylindrical stochastic processes, stochastic integrals and stochastic partial differential equations driven by these cylindrical stochastic processes, mainly in the context of duals of nuclear spaces.