Examples of It\o c\`adl\`ag rough paths
Abstract
Based on a dyadic approximation of It\o integrals, we show the existence of It\o c\`adl\`ag rough paths above general semimartingales, suitable Gaussian processes and non-negative typical price paths. Furthermore, Lyons-Victoir extension theorem for c\`adl\`ag paths is presented, stating that every c\`adl\`ag path of finite p-variation can be lifted to a rough path.
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