Examples of Itô càdlàg rough paths

Liu, Chong; Prömel, David

doi:10.1090/proc/14142

Examples of Itô càdlàg rough paths

Authors: Chong Liu and David J. Prömel
Journal: Proc. Amer. Math. Soc. 146 (2018), 4937-4950
MSC (2010): Primary 60H99, 60G17; Secondary 91G99
DOI: https://doi.org/10.1090/proc/14142
Published electronically: August 8, 2018
MathSciNet review: 3856160
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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 -variation can be lifted to a rough path.

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