Stochastic integration by parts and functional itô calculus by Bally, V, Caramellino, L, Cont, R

Pathwise integration with respect to paths of finite quadratic variation by Ananova, A, Cont, R

“…We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. …”