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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

DOI: https://doi.org/10.1090/proc/14142
Keywords: C\`adl\`ag 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