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.References
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Additional Information
- Chong Liu
- Affiliation: Departement Mathematik, Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland
- Email: chong.liu@math.ethz.ch
- David J. Prömel
- Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
- Email: proemel@maths.ox.ac.uk
- Received by editor(s): September 19, 2017
- Received by editor(s) in revised form: February 12, 2018
- Published electronically: August 8, 2018
- Additional Notes: The second author gratefully acknowledges financial support of the Swiss National Foundation under Grant No. 200021_163014 and was affiliated with ETH Zürich when this project was commenced.
- Communicated by: Zhen-Qing Chen
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4937-4950
- MSC (2010): Primary 60H99, 60G17; Secondary 91G99
- DOI: https://doi.org/10.1090/proc/14142
- MathSciNet review: 3856160