Examples of Itô càdlàg rough paths

Based on a dyadic approximation of Itô integrals, we show the existence of Itô càdlàg rough paths above general semimartingales, suitable Gaussian processes, and nonnegative typical price paths. Furthermore, the Lyons-Victoir extension theorem for càdlàg paths is presented, stating that every càdlàg path of finite p-variation can be lifted to a rough pat