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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 $p$-variation can be lifted to a rough path.


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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

Keywords: Càdlàg rough paths, Gaussian processes, Lyons–Victoir extension theorem, semimartingales, typical price paths
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
Article copyright: © Copyright 2018 American Mathematical Society