Examples of Itô càdlàg rough paths

Liu, Chong; Prömel, David

doi:10.1090/proc/14142

Examples of Itô càdlàg rough paths
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by Chong Liu and David J. Prömel PDF

Proc. Amer. Math. Soc. 146 (2018), 4937-4950 Request permission

Abstract:

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 path.

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