A Fourier approach to pathwise stochastic integration

Abstract

We develop a Fourier approach to rough path integration, based on the series decomposition of continuous functions in terms of Schauder functions. Our approach is rather elementary, the main ingredient being a simple commutator estimate, and it leads to recursive algorithms for the calculation of pathwise stochastic integrals, both of It\^o and of Stratonovich type. We apply it to solve stochastic differential equations in a pathwise manner.