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arXiv · 1709.05988

Examples of It\^o c\`adl\`ag rough paths

Chong Liu·David J. Prömel
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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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Chong Liu, David J. Prömel. 2017-09-18. Examples of It\^o c\`adl\`ag rough paths. https://arxiv.org/abs/1709.05988

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