Skorohod and Stratonovich integrals for controlled processes

Abstract

Given a continuous Gaussian process x which gives rise to a p-geometric rough path for p∈(2,3), and a general continuous process y controlled by x, under proper conditions we establish the relationship between the Skorohod integral ∫0tysd♢xs and the Stratonovich integral ∫0tysdxs. Our strategy is to employ the tools from rough paths theory and Malliavin calculus to analyze discrete sums of the integrals.